Murray Wiki - User contributions [en]

Nils Napp, June 2011

2011-06-22T21:23:53Z

Genti: /* Schedule */

[http://soslab.ee.washington.edu/mw/index.php/User:Napp Nils Napp] will be visiting from Harvard on 27 June (Mon). He will give a talk in my group meeting on some of his recent work at Harvard.

=== Schedule ===

Monday:
* 9:45a - 10:30a: Open (if all other slots are full)
* 10:30a - 11:15a: Open (if all other slots are full)
* 11:15a-12p: Richard, 109 Steele
* 12p-1p: Group meeting presentation, 214 Steele
* 1:15p - 2:00p: Genti Buzi
* 2:00p - 2:45p: Open
* 3:00p - 4:00p: Elisa Franco PhD defense, 107 ANB
* 4:00 - 4:45p: Open

=== Research description ===

Broadly, my research focuses on the control of stochastically interacting things. My goal is to steer global system behavior in the face of random, but tunable, behavior of individual sub components. How do natural systems achieve high reliability while being built from unreliable, stochastic sub components? What is the right level of abstraction for modeling such systems, especially when the number of sub components is large?
I've worked mostly with robotic test-beds where randomness is introduced by choice to give robustness, scalability, or simply to explore control strategies. However, many of the ideas come from my interactions with the synthetic biologists in our research group. Currently, I'm thinking about control strategies for a particular system model, Stochastic Reaction Networks.

Nils Napp, June 2011

2011-06-22T21:22:25Z

Genti: /* Schedule */

[http://soslab.ee.washington.edu/mw/index.php/User:Napp Nils Napp] will be visiting from Harvard on 27 June (Mon). He will give a talk in my group meeting on some of his recent work at Harvard.

=== Schedule ===

Monday:
* 9:45a - 10:30a: Open (if all other slots are full)
* 10:30a - 11:15a: Open (if all other slots are full)
* 11:15a-12p: Richard, 109 Steele
* 12p-1p: Group meeting presentation, 214 Steele
* 1:15p - 2:00p: Genti
* 2:00p - 2:45p: Open
* 3:00p - 4:00p: Elisa Franco PhD defense, 107 ANB
* 4:00 - 4:45p: Open

=== Research description ===

Broadly, my research focuses on the control of stochastically interacting things. My goal is to steer global system behavior in the face of random, but tunable, behavior of individual sub components. How do natural systems achieve high reliability while being built from unreliable, stochastic sub components? What is the right level of abstraction for modeling such systems, especially when the number of sub components is large?
I've worked mostly with robotic test-beds where randomness is introduced by choice to give robustness, scalability, or simply to explore control strategies. However, many of the ideas come from my interactions with the synthetic biologists in our research group. Currently, I'm thinking about control strategies for a particular system model, Stochastic Reaction Networks.

ACM 101/AM 125b/CDS 140a, Winter 2011

2011-03-02T19:51:31Z

Genti:

{| width=100%
|-
| colspan=2 align=center |
Differential Equations and Dynamical Systems__NOTOC__
|- valign=top
| width=50% |
'''Instructors'''
* Richard Murray (CDS/BE)
* Gentian Buzi (CDS)
* Lectures: Tu/Th, 9-10:30, 105 ANB
| width=50% |
'''Teaching Assistants'''
* Molei Tao (CDS)
* Zhaoqian (Steven) Xie (CDS)
* Office hours: Mon 2-3pm, 314 ANB; Wed 12-2pm, 107 ANB
|}

=== Course Description ===
Analytical methods for the formulation and solution of initial value problems for ordinary differential equations. Basics in topics in dynamical systems in Euclidean space, including equilibria, stability, phase diagrams, Lyapunov functions, periodic solutions, Poincaré-Bendixon theory, Poincaré maps. Introduction to simple bifurcations, including Hopf bifurcations, invariant and center manifolds.

===Announcements ===
* 02 Mar 2011: For those interested, we have posted an [[Media:cds140a-wi11-CMTLimitCycleExample.pdf|example]] illustrating the use of CMT and Lyapunov functions.
* 08 Feb 2011: [[Media:cds140a-wi11-hw6.pdf|HW #6]] is now posted; due 17 Feb 2011
* 01 Feb 2011: [[Media:cds140a-wi11-hw5-newstyle.pdf|HW #5]] is now posted; due 10 Feb 2011
* 25 Jan 2011: [[CDS 140a Winter 2011 Homework 4|HW #4]] is now posted; due 3 Feb 2011
* 18 Jan 2011: [[CDS 140a Winter 2011 Homework 3|HW #3]] is now posted; due 27 Jan 2011
* 11 Jan 2011: [[CDS 140a Winter 2011 Homework 2|HW #2]] is now posted; due 20 Jan 2011
* 6 Jan 2011: Office hours for HW #1 will be on 10 Jan (Mon) from 4-6 pm in 235 ANB; office hours for future weeks will be on Wednesdays from 12-2 in 235 ANB
* 6 Jan 2011: Course ombuds: Jeff Amelang and Matanya Horowitz
* 3 Jan 2011: [[CDS 140a Winter 2011 Homework 1|HW #1]] is now posted; due 11 Jan 2011
* 14 Nov 2010: web page creation

=== Lecture Schedule ===

{| width=100% border=1 cellspacing=0 cellpadding=5
|-
| '''Date'''
| '''Topic'''
| '''Reading'''
| '''Homework'''
|- valign=top
|- valign=top
| 4 Jan 6 Jan
| Linear Differential Equations I
* Course overview and administration
* Linear differential equations
* Matrix exponential, diagonalization
* Stable and unstable spaces
* Planar systems, behavior of solutions
|
Perko, 1.1-1.6 
Optional:
* J&S, Ch 1 
* J&S, 2.1-2.5
| [[CDS 140a Winter 2011 Homework 1|HW 1]]
|- valign=top
| 11 Jan 13 Jan
| Linear Differential Equations II
* S + N decomposition, Jordan form
* Stability theory
* Linear systems with inputs (nonhomogeneous systems)
* Boundary value problems
| Perko, 1.7-1.10 + notes
| [[CDS 140a Winter 2011 Homework 2|HW 2]]
|- valign=top
| 18 Jan 20 Jan
| Nonlinear differential equations
* Existence and uniqueness
* Flow of a differential equation
* Linearization
| Perko, 2.1-2.6
| [[CDS 140a Winter 2011 Homework 3|HW 3]]
|- valign=top
| 25 Jan 27 Jan
| Behavior of differential equations
* Stable and unstable manifolds
* Stability of equilibrium points
| Perko, 2.7-2.10
* [[Media:cds140a-wi11-Week4Notes.pdf|Some notes]]
* [[Media:cds140a-wi11-InvManRemark.pdf|Remark on invariant manifolds]]
| | [[CDS 140a Winter 2011 Homework 4|HW 4]]
|- valign=top
| 1 Feb* 3 Feb*
| Non-hyperbolic differential equations
* Lyapunov functions
* Center manifold theorem
| Perko, 2.11-2.13
* [[Media:cds140a-wi11-Week5Notes.pdf|Notes on Lyapunov]]
* [[Media:cds140a-wi11-Week5NotesCMT.pdf|Notes on Center Manifold]]
* [[Media:cds140a-wi11-CMTLimitCycleExample.pdf|An Example (Center Manifold / Limit Cycle)]]
| [[Media:cds140a-wi11-hw5-newstyle.pdf|HW 5]]
|- valign=top
| 8 Feb* 10 Feb
| Hamiltonian systems
* Gradient and Hamiltonian systems
* Energy based stability methods
* Applications
| Perko 2.14 + notes
* [[Media:cds140a-wi11-Week6NotesHamGrad.pdf|Gradient and Hamiltonian Systems]]
* [[Media:cds140a-wi11-Week6NotesLagHamSum.pdf|Lagrangian, Summary]]
| [[Media:cds140a-wi11-hw6.pdf|HW 6]]
|- valign=top
| 15 Feb 17 Feb 22 Feb
| Limit cycles
* Limit sets and attractors
* Periodic orbits and limit cycles
* Poincare' map
* Bendixson criterion for limit cycles in the plane
| Perko, 3.1-3.5, 3.9
* [http://www.cds.caltech.edu/~murray/courses/cds140/wi11/caltech/L7-1_orbits-15Feb11.pdf Lecture notes on orbits and attractors]
* [http://www.cds.caltech.edu/~murray/courses/cds140/wi11/caltech/L7-2_limitcycles-17Feb11.pdf Lecture notes on limit cycles]
* [http://www.cds.caltech.edu/~murray/courses/cds140/wi11/caltech/L7-3_bfs_oscillators.pdf BFS notes on oscillators]
| [[CDS 140a Winter 2011 Homework 7|HW 7]]
|- valign=top
|- valign=top
| 24 Feb 1 Mar 3 Mar
| Bifurcations
* Structural stability
* Bifurcation of equilibrium points
* Hopf bifurcation
| Perko 4.1-4.4 + notes
* [http://www.cds.caltech.edu/~murray/courses/cds140/wi11/caltech/L8-1_parmsens-24Feb11.pdf Lecture notes on structural stability, parameter sensitivity]
* [http://www.cds.caltech.edu/~murray/courses/cds140/wi11/caltech/L8-1_bfs_sensitivity.pdf BFS notes on parameter sensitivity]
* [http://www.cds.caltech.edu/~murray/courses/cds140/wi11/caltech/L8-2_bifurcations-01Mar11.pdf Lecture notes on bifurcations]
| [[CDS 140a Winter 2011 Homework 8|HW 8]]
|- valign=top
| 8 Mar 
| Course review
| 
| 
|}

=== Textbook ===

The primary text for the course (available via the online bookstore) is
{|
|- valign=top
| align=right |  [Perko] 
| L. Perko, Differential Equations and Dynamical Systems, Third Edition. Springer, 2006.
|}

The following additional texts may be useful for some students (on reserve in SFL):
{|
|- valign=top
| align=right |  [J&S] 
| D. Jordan and P. Smith, Nonlinear Ordinary Differential Equations: An Introduction for Scientists and Engineers, Fourth Edition. Oxford University Press, 2007.
|}

=== Grading ===
The ﬁnal grade will be based on homework and a ﬁnal exam:
* Homework (75%) - There will be 9 one-week problem sets, due in class approximately one week after they are assigned. Late homework will not be accepted without prior permission from the instructor.
* Final exam (25%) - The ﬁnal will be handed out the last day of class and is due back at the end of ﬁnals week. Open book, time limit to be decided (likely N hours over a 4-8N hour period).

The lowest homework score you receive will be dropped in computing your homework average. In addition, if your score on the ﬁnal is higher than the weighted average of your homework and ﬁnal, your ﬁnal will be used to determine your course grade.

=== Collaboration Policy ===
Collaboration on homework assignments is encouraged. You may consult outside reference materials, other students, the TA, or the instructor. Use of solutions from previous years in the course or from other external sources is not allowed. All solutions that are handed should reﬂect your understanding of the subject matter at the time of writing.

No collaboration is allowed on the ﬁnal exam.

== Old Announcements ==

ACM 101/AM 125b/CDS 140a, Winter 2011

2011-03-02T07:20:31Z

Genti: /* Lecture Schedule */

{| width=100%
|-
| colspan=2 align=center |
Differential Equations and Dynamical Systems__NOTOC__
|- valign=top
| width=50% |
'''Instructors'''
* Richard Murray (CDS/BE)
* Gentian Buzi (CDS)
* Lectures: Tu/Th, 9-10:30, 105 ANB
| width=50% |
'''Teaching Assistants'''
* Molei Tao (CDS)
* Zhaoqian (Steven) Xie (CDS)
* Office hours: Mon 2-3pm, 314 ANB; Wed 12-2pm, 107 ANB
|}

=== Course Description ===
Analytical methods for the formulation and solution of initial value problems for ordinary differential equations. Basics in topics in dynamical systems in Euclidean space, including equilibria, stability, phase diagrams, Lyapunov functions, periodic solutions, Poincaré-Bendixon theory, Poincaré maps. Introduction to simple bifurcations, including Hopf bifurcations, invariant and center manifolds.

===Announcements ===
* 08 Feb 2011: [[Media:cds140a-wi11-hw6.pdf|HW #6]] is now posted; due 17 Feb 2011
* 01 Feb 2011: [[Media:cds140a-wi11-hw5-newstyle.pdf|HW #5]] is now posted; due 10 Feb 2011
* 25 Jan 2011: [[CDS 140a Winter 2011 Homework 4|HW #4]] is now posted; due 3 Feb 2011
* 18 Jan 2011: [[CDS 140a Winter 2011 Homework 3|HW #3]] is now posted; due 27 Jan 2011
* 11 Jan 2011: [[CDS 140a Winter 2011 Homework 2|HW #2]] is now posted; due 20 Jan 2011
* 6 Jan 2011: Office hours for HW #1 will be on 10 Jan (Mon) from 4-6 pm in 235 ANB; office hours for future weeks will be on Wednesdays from 12-2 in 235 ANB
* 6 Jan 2011: Course ombuds: Jeff Amelang and Matanya Horowitz
* 3 Jan 2011: [[CDS 140a Winter 2011 Homework 1|HW #1]] is now posted; due 11 Jan 2011
* 14 Nov 2010: web page creation

=== Lecture Schedule ===

{| width=100% border=1 cellspacing=0 cellpadding=5
|-
| '''Date'''
| '''Topic'''
| '''Reading'''
| '''Homework'''
|- valign=top
|- valign=top
| 4 Jan 6 Jan
| Linear Differential Equations I
* Course overview and administration
* Linear differential equations
* Matrix exponential, diagonalization
* Stable and unstable spaces
* Planar systems, behavior of solutions
|
Perko, 1.1-1.6 
Optional:
* J&S, Ch 1 
* J&S, 2.1-2.5
| [[CDS 140a Winter 2011 Homework 1|HW 1]]
|- valign=top
| 11 Jan 13 Jan
| Linear Differential Equations II
* S + N decomposition, Jordan form
* Stability theory
* Linear systems with inputs (nonhomogeneous systems)
* Boundary value problems
| Perko, 1.7-1.10 + notes
| [[CDS 140a Winter 2011 Homework 2|HW 2]]
|- valign=top
| 18 Jan 20 Jan
| Nonlinear differential equations
* Existence and uniqueness
* Flow of a differential equation
* Linearization
| Perko, 2.1-2.6
| [[CDS 140a Winter 2011 Homework 3|HW 3]]
|- valign=top
| 25 Jan 27 Jan
| Behavior of differential equations
* Stable and unstable manifolds
* Stability of equilibrium points
| Perko, 2.7-2.10
* [[Media:cds140a-wi11-Week4Notes.pdf|Some notes]]
* [[Media:cds140a-wi11-InvManRemark.pdf|Remark on invariant manifolds]]
| | [[CDS 140a Winter 2011 Homework 4|HW 4]]
|- valign=top
| 1 Feb* 3 Feb*
| Non-hyperbolic differential equations
* Lyapunov functions
* Center manifold theorem
| Perko, 2.11-2.13
* [[Media:cds140a-wi11-Week5Notes.pdf|Notes on Lyapunov]]
* [[Media:cds140a-wi11-Week5NotesCMT.pdf|Notes on Center Manifold]]
* [[Media:cds140a-wi11-CMTLimitCycleExample.pdf|An Example (Center Manifold / Limit Cycle)]]
| [[Media:cds140a-wi11-hw5-newstyle.pdf|HW 5]]
|- valign=top
| 8 Feb* 10 Feb
| Hamiltonian systems
* Gradient and Hamiltonian systems
* Energy based stability methods
* Applications
| Perko 2.14 + notes
* [[Media:cds140a-wi11-Week6NotesHamGrad.pdf|Gradient and Hamiltonian Systems]]
* [[Media:cds140a-wi11-Week6NotesLagHamSum.pdf|Lagrangian, Summary]]
| [[Media:cds140a-wi11-hw6.pdf|HW 6]]
|- valign=top
| 15 Feb 17 Feb 22 Feb
| Limit cycles
* Limit sets and attractors
* Periodic orbits and limit cycles
* Poincare' map
* Bendixson criterion for limit cycles in the plane
| Perko, 3.1-3.5, 3.9
* [http://www.cds.caltech.edu/~murray/courses/cds140/wi11/caltech/L7-1_orbits-15Feb11.pdf Lecture notes on orbits and attractors]
* [http://www.cds.caltech.edu/~murray/courses/cds140/wi11/caltech/L7-2_limitcycles-17Feb11.pdf Lecture notes on limit cycles]
* [http://www.cds.caltech.edu/~murray/courses/cds140/wi11/caltech/L7-3_bfs_oscillators.pdf BFS notes on oscillators]
| [[CDS 140a Winter 2011 Homework 7|HW 7]]
|- valign=top
|- valign=top
| 24 Feb 1 Mar 3 Mar
| Bifurcations
* Structural stability
* Bifurcation of equilibrium points
* Hopf bifurcation
| Perko 4.1-4.4 + notes
* [http://www.cds.caltech.edu/~murray/courses/cds140/wi11/caltech/L8-1_parmsens-24Feb11.pdf Lecture notes on structural stability, parameter sensitivity]
* [http://www.cds.caltech.edu/~murray/courses/cds140/wi11/caltech/L8-1_bfs_sensitivity.pdf BFS notes on parameter sensitivity]
* [http://www.cds.caltech.edu/~murray/courses/cds140/wi11/caltech/L8-2_bifurcations-01Mar11.pdf Lecture notes on bifurcations]
| [[CDS 140a Winter 2011 Homework 8|HW 8]]
|- valign=top
| 8 Mar 
| Course review
| 
| 
|}

=== Textbook ===

The primary text for the course (available via the online bookstore) is
{|
|- valign=top
| align=right |  [Perko] 
| L. Perko, Differential Equations and Dynamical Systems, Third Edition. Springer, 2006.
|}

The following additional texts may be useful for some students (on reserve in SFL):
{|
|- valign=top
| align=right |  [J&S] 
| D. Jordan and P. Smith, Nonlinear Ordinary Differential Equations: An Introduction for Scientists and Engineers, Fourth Edition. Oxford University Press, 2007.
|}

=== Grading ===
The ﬁnal grade will be based on homework and a ﬁnal exam:
* Homework (75%) - There will be 9 one-week problem sets, due in class approximately one week after they are assigned. Late homework will not be accepted without prior permission from the instructor.
* Final exam (25%) - The ﬁnal will be handed out the last day of class and is due back at the end of ﬁnals week. Open book, time limit to be decided (likely N hours over a 4-8N hour period).

The lowest homework score you receive will be dropped in computing your homework average. In addition, if your score on the ﬁnal is higher than the weighted average of your homework and ﬁnal, your ﬁnal will be used to determine your course grade.

=== Collaboration Policy ===
Collaboration on homework assignments is encouraged. You may consult outside reference materials, other students, the TA, or the instructor. Use of solutions from previous years in the course or from other external sources is not allowed. All solutions that are handed should reﬂect your understanding of the subject matter at the time of writing.

No collaboration is allowed on the ﬁnal exam.

== Old Announcements ==

File:Cds140a-wi11-CMTLimitCycleExample.pdf

2011-03-02T07:17:28Z

Genti:

CDS 140a Winter 2011 Homework 7

2011-02-22T17:02:07Z

Genti:

{{CDS homework
| instructor = R. Murray, G. Buzi
| course = ACM 101/AM 125a/CDS 140a
| semester = Winter 2011
| title = Problem Set #7
| issued = 15 Feb 2011
| due = 1 Mar 2011 (Tue)
}}

'''Note:''' In the upper left hand corner of the ''second'' page of your homework set, please put the number of hours that you spent on
this homework set (including reading).

# Perko, Section 3.2, Exercise 5
# Perko, Section 3.3, Exercise 8
# Perko, Section 3.4, Exercise 1
# Perko, Section 3.5, Exercise 1
# Perko, Section 3.5, Exercise 5
# Perko, Section 3.9, Exercise 4a

ACM 101/AM 125b/CDS 140a, Winter 2011

2011-02-15T20:53:15Z

Genti: /* Lecture Schedule */

{| width=100%
|-
| colspan=2 align=center |
Differential Equations and Dynamical Systems__NOTOC__
|- valign=top
| width=50% |
'''Instructors'''
* Richard Murray (CDS/BE)
* Gentian Buzi (CDS)
* Lectures: Tu/Th, 9-10:30, 105 ANB
| width=50% |
'''Teaching Assistants'''
* Molei Tao (CDS)
* Zhaoqian (Steven) Xie (CDS)
* Office hours: Mon 2-3pm, 314 ANB; Wed 12-2pm, 107 ANB
|}

=== Course Description ===
Analytical methods for the formulation and solution of initial value problems for ordinary differential equations. Basics in topics in dynamical systems in Euclidean space, including equilibria, stability, phase diagrams, Lyapunov functions, periodic solutions, Poincaré-Bendixon theory, Poincaré maps. Introduction to simple bifurcations, including Hopf bifurcations, invariant and center manifolds.

===Announcements ===
* 08 Feb 2011: [[Media:cds140a-wi11-hw6.pdf|HW #6]] is now posted; due 17 Feb 2011
* 01 Feb 2011: [[Media:cds140a-wi11-hw5-newstyle.pdf|HW #5]] is now posted; due 10 Feb 2011
* 25 Jan 2011: [[CDS 140a Winter 2011 Homework 4|HW #4]] is now posted; due 3 Feb 2011
* 18 Jan 2011: [[CDS 140a Winter 2011 Homework 3|HW #3]] is now posted; due 27 Jan 2011
* 11 Jan 2011: [[CDS 140a Winter 2011 Homework 2|HW #2]] is now posted; due 20 Jan 2011
* 6 Jan 2011: Office hours for HW #1 will be on 10 Jan (Mon) from 4-6 pm in 235 ANB; office hours for future weeks will be on Wednesdays from 12-2 in 235 ANB
* 6 Jan 2011: Course ombuds: Jeff Amelang and Matanya Horowitz
* 3 Jan 2011: [[CDS 140a Winter 2011 Homework 1|HW #1]] is now posted; due 11 Jan 2011
* 14 Nov 2010: web page creation

=== Lecture Schedule ===

{| width=100% border=1 cellspacing=0 cellpadding=5
|-
| '''Week'''
| '''Date'''
| '''Topic'''
| '''Reading'''
| '''Homework'''
|- valign=top
|- valign=top
| 1
| 4 Jan 6 Jan
| Linear Differential Equations I
* Course overview and administration
* Linear differential equations
* Matrix exponential, diagonalization
* Stable and unstable spaces
* Planar systems, behavior of solutions
|
Perko, 1.1-1.6 
Optional:
* J&S, Ch 1 
* J&S, 2.1-2.5
| [[CDS 140a Winter 2011 Homework 1|HW 1]]
|- valign=top
| 2
| 11 Jan 13 Jan
| Linear Differential Equations II
* S + N decomposition, Jordan form
* Stability theory
* Linear systems with inputs (nonhomogeneous systems)
* Boundary value problems
| Perko, 1.7-1.10 + notes
| [[CDS 140a Winter 2011 Homework 2|HW 2]]
|- valign=top
| 3
| 18 Jan 20 Jan
| Nonlinear differential equations
* Existence and uniqueness
* Flow of a differential equation
* Linearization
| Perko, 2.1-2.6
| [[CDS 140a Winter 2011 Homework 3|HW 3]]
|- valign=top
| 4
| 25 Jan 27 Jan
| Behavior of differential equations
* Stable and unstable manifolds
* Stability of equilibrium points
| Perko, 2.7-2.10
* [[Media:cds140a-wi11-Week4Notes.pdf|Some notes]]
* [[Media:cds140a-wi11-InvManRemark.pdf|Remark on invariant manifolds]]
| | [[CDS 140a Winter 2011 Homework 4|HW 4]]
|- valign=top
| 5
| 1 Feb* 3 Feb*
| Non-hyperbolic differential equations
* Lyapunov functions
* Center manifold theorem
| Perko, 2.11-2.13
* [[Media:cds140a-wi11-Week5Notes.pdf|Notes on Lyapunov]]
* [[Media:cds140a-wi11-Week5NotesCMT.pdf|Notes on Center Manifold]]
| [[Media:cds140a-wi11-hw5-newstyle.pdf|HW 5]]
|- valign=top
| 6
| 8 Feb* 10 Feb
| Hamiltonian systems
* Gradient and Hamiltonian systems
* Energy based stability methods
* Applications
| Perko 2.14 + notes
* [[Media:cds140a-wi11-Week6NotesHamGrad.pdf|Gradient and Hamiltonian Systems]]
* [[Media:cds140a-wi11-Week6NotesLagHamSum.pdf|Lagrangian, Summary]]
| [[Media:cds140a-wi11-hw6.pdf|HW 6]]
|- valign=top
| 7
| 15 Feb 17 Feb
| Limit cycles
* Limit sets and attractors
* Periodic orbits and limit cycles
* Poincare' map
* Bendixson criterion for limit cycles in the plane
| Perko, 3.1-3.5, 3.9
* [http://www.cds.caltech.edu/~murray/courses/cds140/wi11/caltech/L7-1_orbits-15Feb11.pdf Tue lecture notes]
| [[CDS 140a Winter 2011 Homework 7|HW 7]]
|- valign=top
| 8
| 22 Feb 24 Feb
| Bifurcations
* Structural stability
* Bifurcation of equilibrium points
* Hopf bifurcation
| Perko 4.1-4.4
| 
|- valign=top
| 9
| 1 Mar 3 Mar
| Advanced topics
* Higher co-dimension bifurcations
* Homoclinic bifurcation
| Perko, 4-3, 4.5-4.8, notes
| 
|- valign=top
| 10
| 8 Mar 
| Course review
| 
| 
|}

=== Textbook ===

The primary text for the course (available via the online bookstore) is
{|
|- valign=top
| align=right |  [Perko] 
| L. Perko, Differential Equations and Dynamical Systems, Third Edition. Springer, 2006.
|}

The following additional texts may be useful for some students (on reserve in SFL):
{|
|- valign=top
| align=right |  [J&S] 
| D. Jordan and P. Smith, Nonlinear Ordinary Differential Equations: An Introduction for Scientists and Engineers, Fourth Edition. Oxford University Press, 2007.
|}

=== Grading ===
The ﬁnal grade will be based on homework and a ﬁnal exam:
* Homework (75%) - There will be 9 one-week problem sets, due in class approximately one week after they are assigned. Late homework will not be accepted without prior permission from the instructor.
* Final exam (25%) - The ﬁnal will be handed out the last day of class and is due back at the end of ﬁnals week. Open book, time limit to be decided (likely N hours over a 4-8N hour period).

The lowest homework score you receive will be dropped in computing your homework average. In addition, if your score on the ﬁnal is higher than the weighted average of your homework and ﬁnal, your ﬁnal will be used to determine your course grade.

=== Collaboration Policy ===
Collaboration on homework assignments is encouraged. You may consult outside reference materials, other students, the TA, or the instructor. Use of solutions from previous years in the course or from other external sources is not allowed. All solutions that are handed should reﬂect your understanding of the subject matter at the time of writing.

No collaboration is allowed on the ﬁnal exam.

== Old Announcements ==

File:Cds140a-wi11-InvManRemark.pdf

2011-02-15T20:52:18Z

Genti:

ACM 101/AM 125b/CDS 140a, Winter 2011

2011-02-13T01:10:34Z

Genti: /* Lecture Schedule */

{| width=100%
|-
| colspan=2 align=center |
Differential Equations and Dynamical Systems__NOTOC__
|- valign=top
| width=50% |
'''Instructors'''
* Richard Murray (CDS/BE)
* Gentian Buzi (CDS)
* Lectures: Tu/Th, 9-10:30, 105 ANB
| width=50% |
'''Teaching Assistants'''
* Molei Tao (CDS)
* Zhaoqian (Steven) Xie (CDS)
* Office hours: Mon 2-3pm, 314 ANB; Wed 12-2pm, 107 ANB
|}

=== Course Description ===
Analytical methods for the formulation and solution of initial value problems for ordinary differential equations. Basics in topics in dynamical systems in Euclidean space, including equilibria, stability, phase diagrams, Lyapunov functions, periodic solutions, Poincaré-Bendixon theory, Poincaré maps. Introduction to simple bifurcations, including Hopf bifurcations, invariant and center manifolds.

===Announcements ===
* 08 Feb 2011: [[Media:cds140a-wi11-hw6.pdf|HW #6]] is now posted; due 17 Feb 2011
* 01 Feb 2011: [[Media:cds140a-wi11-hw5-newstyle.pdf|HW #5]] is now posted; due 10 Feb 2011
* 25 Jan 2011: [[CDS 140a Winter 2011 Homework 4|HW #4]] is now posted; due 3 Feb 2011
* 18 Jan 2011: [[CDS 140a Winter 2011 Homework 3|HW #3]] is now posted; due 27 Jan 2011
* 11 Jan 2011: [[CDS 140a Winter 2011 Homework 2|HW #2]] is now posted; due 20 Jan 2011
* 6 Jan 2011: Office hours for HW #1 will be on 10 Jan (Mon) from 4-6 pm in 235 ANB; office hours for future weeks will be on Wednesdays from 12-2 in 235 ANB
* 6 Jan 2011: Course ombuds: Jeff Amelang and Matanya Horowitz
* 3 Jan 2011: [[CDS 140a Winter 2011 Homework 1|HW #1]] is now posted; due 11 Jan 2011
* 14 Nov 2010: web page creation

=== Lecture Schedule ===

{| width=100% border=1 cellspacing=0 cellpadding=5
|-
| '''Week'''
| '''Date'''
| '''Topic'''
| '''Reading'''
| '''Homework'''
|- valign=top
|- valign=top
| 1
| 4 Jan 6 Jan
| Linear Differential Equations I
* Course overview and administration
* Linear differential equations
* Matrix exponential, diagonalization
* Stable and unstable spaces
* Planar systems, behavior of solutions
|
Perko, 1.1-1.6 
Optional:
* J&S, Ch 1 
* J&S, 2.1-2.5
| [[CDS 140a Winter 2011 Homework 1|HW 1]]
|- valign=top
| 2
| 11 Jan 13 Jan
| Linear Differential Equations II
* S + N decomposition, Jordan form
* Stability theory
* Linear systems with inputs (nonhomogeneous systems)
* Boundary value problems
| Perko, 1.7-1.10 + notes
| [[CDS 140a Winter 2011 Homework 2|HW 2]]
|- valign=top
| 3
| 18 Jan 20 Jan
| Nonlinear differential equations
* Existence and uniqueness
* Flow of a differential equation
* Linearization
| Perko, 2.1-2.6
| [[CDS 140a Winter 2011 Homework 3|HW 3]]
|- valign=top
| 4
| 25 Jan 27 Jan
| Behavior of differential equations
* Stable and unstable manifolds
* Stability of equilibrium points
| Perko, 2.7-2.10
* [[Media:cds140a-wi11-Week4Notes.pdf|Some notes]]
| | [[CDS 140a Winter 2011 Homework 4|HW 4]]
|- valign=top
| 5
| 1 Feb* 3 Feb*
| Non-hyperbolic differential equations
* Lyapunov functions
* Center manifold theorem
| Perko, 2.11-2.13
* [[Media:cds140a-wi11-Week5Notes.pdf|Notes on Lyapunov]]
* [[Media:cds140a-wi11-Week5NotesCMT.pdf|Notes on Center Manifold]]
| [[Media:cds140a-wi11-hw5-newstyle.pdf|HW 5]]
|- valign=top
| 6
| 8 Feb* 10 Feb
| Hamiltonian systems
* Gradient and Hamiltonian systems
* Energy based stability methods
* Applications
| Perko 2.14 + notes
* [[Media:cds140a-wi11-Week6NotesHamGrad.pdf|Gradient and Hamiltonian Systems]]
* [[Media:cds140a-wi11-Week6NotesLagHamSum.pdf|Lagrangian, Summary]]
| [[Media:cds140a-wi11-hw6.pdf|HW 6]]
|- valign=top
| 7
| 15 Feb 17 Feb
| Limit cycles
* Limit sets and attractors
* Periodic orbits and limit cycles
* Poincare' map
* Bendixson criterion for limit cycles in the plane
| Perko, 3.2-3.4, 3.9
| 
|- valign=top
| 8
| 22 Feb 24 Feb
| Bifurcations
* Structural stability
* Bifurcation of equilibrium points
* Hopf bifurcation
| Perko 4.1-4.4
| 
|- valign=top
| 9
| 1 Mar 3 Mar
| Advanced topics
* Higher co-dimension bifurcations
* Homoclinic bifurcation
| Perko, 4-3, 4.5-4.8, notes
| 
|- valign=top
| 10
| 8 Mar 
| Course review
| 
| 
|}

=== Textbook ===

The primary text for the course (available via the online bookstore) is
{|
|- valign=top
| align=right |  [Perko] 
| L. Perko, Differential Equations and Dynamical Systems, Third Edition. Springer, 2006.
|}

The following additional texts may be useful for some students (on reserve in SFL):
{|
|- valign=top
| align=right |  [J&S] 
| D. Jordan and P. Smith, Nonlinear Ordinary Differential Equations: An Introduction for Scientists and Engineers, Fourth Edition. Oxford University Press, 2007.
|}

=== Grading ===
The ﬁnal grade will be based on homework and a ﬁnal exam:
* Homework (75%) - There will be 9 one-week problem sets, due in class approximately one week after they are assigned. Late homework will not be accepted without prior permission from the instructor.
* Final exam (25%) - The ﬁnal will be handed out the last day of class and is due back at the end of ﬁnals week. Open book, time limit to be decided (likely N hours over a 4-8N hour period).

The lowest homework score you receive will be dropped in computing your homework average. In addition, if your score on the ﬁnal is higher than the weighted average of your homework and ﬁnal, your ﬁnal will be used to determine your course grade.

=== Collaboration Policy ===
Collaboration on homework assignments is encouraged. You may consult outside reference materials, other students, the TA, or the instructor. Use of solutions from previous years in the course or from other external sources is not allowed. All solutions that are handed should reﬂect your understanding of the subject matter at the time of writing.

No collaboration is allowed on the ﬁnal exam.

== Old Announcements ==

File:Cds140a-wi11-Week6NotesLagHamSum.pdf

2011-02-13T01:09:45Z

Genti:

ACM 101/AM 125b/CDS 140a, Winter 2011

2011-02-09T06:33:43Z

Genti: /* Lecture Schedule */

{| width=100%
|-
| colspan=2 align=center |
Differential Equations and Dynamical Systems__NOTOC__
|- valign=top
| width=50% |
'''Instructors'''
* Richard Murray (CDS/BE)
* Gentian Buzi (CDS)
* Lectures: Tu/Th, 9-10:30, 105 ANB
| width=50% |
'''Teaching Assistants'''
* Molei Tao (CDS)
* Zhaoqian (Steven) Xie (CDS)
* Office hours: Mon 2-3pm, 314 ANB; Wed 12-2pm, 107 ANB
|}

=== Course Description ===
Analytical methods for the formulation and solution of initial value problems for ordinary differential equations. Basics in topics in dynamical systems in Euclidean space, including equilibria, stability, phase diagrams, Lyapunov functions, periodic solutions, Poincaré-Bendixon theory, Poincaré maps. Introduction to simple bifurcations, including Hopf bifurcations, invariant and center manifolds.

===Announcements ===
* 08 Feb 2011: [[Media:cds140a-wi11-hw6.pdf|HW #6]] is now posted; due 17 Feb 2011
* 01 Feb 2011: [[Media:cds140a-wi11-hw5-newstyle.pdf|HW #5]] is now posted; due 10 Feb 2011
* 25 Jan 2011: [[CDS 140a Winter 2011 Homework 4|HW #4]] is now posted; due 3 Feb 2011
* 18 Jan 2011: [[CDS 140a Winter 2011 Homework 3|HW #3]] is now posted; due 27 Jan 2011
* 11 Jan 2011: [[CDS 140a Winter 2011 Homework 2|HW #2]] is now posted; due 20 Jan 2011
* 6 Jan 2011: Office hours for HW #1 will be on 10 Jan (Mon) from 4-6 pm in 235 ANB; office hours for future weeks will be on Wednesdays from 12-2 in 235 ANB
* 6 Jan 2011: Course ombuds: Jeff Amelang and Matanya Horowitz
* 3 Jan 2011: [[CDS 140a Winter 2011 Homework 1|HW #1]] is now posted; due 11 Jan 2011
* 14 Nov 2010: web page creation

=== Lecture Schedule ===

{| width=100% border=1 cellspacing=0 cellpadding=5
|-
| '''Week'''
| '''Date'''
| '''Topic'''
| '''Reading'''
| '''Homework'''
|- valign=top
|- valign=top
| 1
| 4 Jan 6 Jan
| Linear Differential Equations I
* Course overview and administration
* Linear differential equations
* Matrix exponential, diagonalization
* Stable and unstable spaces
* Planar systems, behavior of solutions
|
Perko, 1.1-1.6 
Optional:
* J&S, Ch 1 
* J&S, 2.1-2.5
| [[CDS 140a Winter 2011 Homework 1|HW 1]]
|- valign=top
| 2
| 11 Jan 13 Jan
| Linear Differential Equations II
* S + N decomposition, Jordan form
* Stability theory
* Linear systems with inputs (nonhomogeneous systems)
* Boundary value problems
| Perko, 1.7-1.10 + notes
| [[CDS 140a Winter 2011 Homework 2|HW 2]]
|- valign=top
| 3
| 18 Jan 20 Jan
| Nonlinear differential equations
* Existence and uniqueness
* Flow of a differential equation
* Linearization
| Perko, 2.1-2.6
| [[CDS 140a Winter 2011 Homework 3|HW 3]]
|- valign=top
| 4
| 25 Jan 27 Jan
| Behavior of differential equations
* Stable and unstable manifolds
* Stability of equilibrium points
| Perko, 2.7-2.10
* [[Media:cds140a-wi11-Week4Notes.pdf|Some notes]]
| | [[CDS 140a Winter 2011 Homework 4|HW 4]]
|- valign=top
| 5
| 1 Feb* 3 Feb*
| Non-hyperbolic differential equations
* Lyapunov functions
* Center manifold theorem
| Perko, 2.11-2.13
* [[Media:cds140a-wi11-Week5Notes.pdf|Notes on Lyapunov]]
* [[Media:cds140a-wi11-Week5NotesCMT.pdf|Notes on Center Manifold]]
| [[Media:cds140a-wi11-hw5-newstyle.pdf|HW 5]]
|- valign=top
| 6
| 8 Feb* 10 Feb
| Hamiltonian systems
* Gradient and Hamiltonian systems
* Energy based stability methods
* Applications
| Perko 2.14 + notes
* [[Media:cds140a-wi11-Week6NotesHamGrad.pdf|Gradient and Hamiltonian Systems]]
| [[Media:cds140a-wi11-hw6.pdf|HW 6]]
|- valign=top
| 7
| 15 Feb 17 Feb
| Limit cycles
* Limit sets and attractors
* Periodic orbits and limit cycles
* Poincare' map
* Bendixson criterion for limit cycles in the plane
| Perko, 3.2-3.4, 3.9
| 
|- valign=top
| 8
| 22 Feb 24 Feb
| Bifurcations
* Structural stability
* Bifurcation of equilibrium points
* Hopf bifurcation
| Perko 4.1-4.4
| 
|- valign=top
| 9
| 1 Mar 3 Mar
| Advanced topics
* Higher co-dimension bifurcations
* Homoclinic bifurcation
| Perko, 4-3, 4.5-4.8, notes
| 
|- valign=top
| 10
| 8 Mar 
| Course review
| 
| 
|}

=== Textbook ===

The primary text for the course (available via the online bookstore) is
{|
|- valign=top
| align=right |  [Perko] 
| L. Perko, Differential Equations and Dynamical Systems, Third Edition. Springer, 2006.
|}

The following additional texts may be useful for some students (on reserve in SFL):
{|
|- valign=top
| align=right |  [J&S] 
| D. Jordan and P. Smith, Nonlinear Ordinary Differential Equations: An Introduction for Scientists and Engineers, Fourth Edition. Oxford University Press, 2007.
|}

=== Grading ===
The ﬁnal grade will be based on homework and a ﬁnal exam:
* Homework (75%) - There will be 9 one-week problem sets, due in class approximately one week after they are assigned. Late homework will not be accepted without prior permission from the instructor.
* Final exam (25%) - The ﬁnal will be handed out the last day of class and is due back at the end of ﬁnals week. Open book, time limit to be decided (likely N hours over a 4-8N hour period).

The lowest homework score you receive will be dropped in computing your homework average. In addition, if your score on the ﬁnal is higher than the weighted average of your homework and ﬁnal, your ﬁnal will be used to determine your course grade.

=== Collaboration Policy ===
Collaboration on homework assignments is encouraged. You may consult outside reference materials, other students, the TA, or the instructor. Use of solutions from previous years in the course or from other external sources is not allowed. All solutions that are handed should reﬂect your understanding of the subject matter at the time of writing.

No collaboration is allowed on the ﬁnal exam.

== Old Announcements ==

File:Cds140a-wi11-Week6NotesHamGrad.pdf

2011-02-09T06:32:40Z

Genti:

ACM 101/AM 125b/CDS 140a, Winter 2011

2011-02-09T06:24:34Z

Genti:

{| width=100%
|-
| colspan=2 align=center |
Differential Equations and Dynamical Systems__NOTOC__
|- valign=top
| width=50% |
'''Instructors'''
* Richard Murray (CDS/BE)
* Gentian Buzi (CDS)
* Lectures: Tu/Th, 9-10:30, 105 ANB
| width=50% |
'''Teaching Assistants'''
* Molei Tao (CDS)
* Zhaoqian (Steven) Xie (CDS)
* Office hours: Mon 2-3pm, 314 ANB; Wed 12-2pm, 107 ANB
|}

=== Course Description ===
Analytical methods for the formulation and solution of initial value problems for ordinary differential equations. Basics in topics in dynamical systems in Euclidean space, including equilibria, stability, phase diagrams, Lyapunov functions, periodic solutions, Poincaré-Bendixon theory, Poincaré maps. Introduction to simple bifurcations, including Hopf bifurcations, invariant and center manifolds.

===Announcements ===
* 08 Feb 2011: [[Media:cds140a-wi11-hw6.pdf|HW #6]] is now posted; due 17 Feb 2011
* 01 Feb 2011: [[Media:cds140a-wi11-hw5-newstyle.pdf|HW #5]] is now posted; due 10 Feb 2011
* 25 Jan 2011: [[CDS 140a Winter 2011 Homework 4|HW #4]] is now posted; due 3 Feb 2011
* 18 Jan 2011: [[CDS 140a Winter 2011 Homework 3|HW #3]] is now posted; due 27 Jan 2011
* 11 Jan 2011: [[CDS 140a Winter 2011 Homework 2|HW #2]] is now posted; due 20 Jan 2011
* 6 Jan 2011: Office hours for HW #1 will be on 10 Jan (Mon) from 4-6 pm in 235 ANB; office hours for future weeks will be on Wednesdays from 12-2 in 235 ANB
* 6 Jan 2011: Course ombuds: Jeff Amelang and Matanya Horowitz
* 3 Jan 2011: [[CDS 140a Winter 2011 Homework 1|HW #1]] is now posted; due 11 Jan 2011
* 14 Nov 2010: web page creation

=== Lecture Schedule ===

{| width=100% border=1 cellspacing=0 cellpadding=5
|-
| '''Week'''
| '''Date'''
| '''Topic'''
| '''Reading'''
| '''Homework'''
|- valign=top
|- valign=top
| 1
| 4 Jan 6 Jan
| Linear Differential Equations I
* Course overview and administration
* Linear differential equations
* Matrix exponential, diagonalization
* Stable and unstable spaces
* Planar systems, behavior of solutions
|
Perko, 1.1-1.6 
Optional:
* J&S, Ch 1 
* J&S, 2.1-2.5
| [[CDS 140a Winter 2011 Homework 1|HW 1]]
|- valign=top
| 2
| 11 Jan 13 Jan
| Linear Differential Equations II
* S + N decomposition, Jordan form
* Stability theory
* Linear systems with inputs (nonhomogeneous systems)
* Boundary value problems
| Perko, 1.7-1.10 + notes
| [[CDS 140a Winter 2011 Homework 2|HW 2]]
|- valign=top
| 3
| 18 Jan 20 Jan
| Nonlinear differential equations
* Existence and uniqueness
* Flow of a differential equation
* Linearization
| Perko, 2.1-2.6
| [[CDS 140a Winter 2011 Homework 3|HW 3]]
|- valign=top
| 4
| 25 Jan 27 Jan
| Behavior of differential equations
* Stable and unstable manifolds
* Stability of equilibrium points
| Perko, 2.7-2.10
* [[Media:cds140a-wi11-Week4Notes.pdf|Some notes]]
| | [[CDS 140a Winter 2011 Homework 4|HW 4]]
|- valign=top
| 5
| 1 Feb* 3 Feb*
| Non-hyperbolic differential equations
* Lyapunov functions
* Center manifold theorem
| Perko, 2.11-2.13
* [[Media:cds140a-wi11-Week5Notes.pdf|Notes on Lyapunov]]
* [[Media:cds140a-wi11-Week5NotesCMT.pdf|Notes on Center Manifold]]
| [[Media:cds140a-wi11-hw5-newstyle.pdf|HW 5]]
|- valign=top
| 6
| 8 Feb* 10 Feb
| Hamiltonian systems
* Gradient and Hamiltonian systems
* Energy based stability methods
* Applications
| Perko 2.14 + notes
| [[Media:cds140a-wi11-hw6.pdf|HW 6]]
|- valign=top
| 7
| 15 Feb 17 Feb
| Limit cycles
* Limit sets and attractors
* Periodic orbits and limit cycles
* Poincare' map
* Bendixson criterion for limit cycles in the plane
| Perko, 3.2-3.4, 3.9
| 
|- valign=top
| 8
| 22 Feb 24 Feb
| Bifurcations
* Structural stability
* Bifurcation of equilibrium points
* Hopf bifurcation
| Perko 4.1-4.4
| 
|- valign=top
| 9
| 1 Mar 3 Mar
| Advanced topics
* Higher co-dimension bifurcations
* Homoclinic bifurcation
| Perko, 4-3, 4.5-4.8, notes
| 
|- valign=top
| 10
| 8 Mar 
| Course review
| 
| 
|}

=== Textbook ===

The primary text for the course (available via the online bookstore) is
{|
|- valign=top
| align=right |  [Perko] 
| L. Perko, Differential Equations and Dynamical Systems, Third Edition. Springer, 2006.
|}

The following additional texts may be useful for some students (on reserve in SFL):
{|
|- valign=top
| align=right |  [J&S] 
| D. Jordan and P. Smith, Nonlinear Ordinary Differential Equations: An Introduction for Scientists and Engineers, Fourth Edition. Oxford University Press, 2007.
|}

=== Grading ===
The ﬁnal grade will be based on homework and a ﬁnal exam:
* Homework (75%) - There will be 9 one-week problem sets, due in class approximately one week after they are assigned. Late homework will not be accepted without prior permission from the instructor.
* Final exam (25%) - The ﬁnal will be handed out the last day of class and is due back at the end of ﬁnals week. Open book, time limit to be decided (likely N hours over a 4-8N hour period).

The lowest homework score you receive will be dropped in computing your homework average. In addition, if your score on the ﬁnal is higher than the weighted average of your homework and ﬁnal, your ﬁnal will be used to determine your course grade.

=== Collaboration Policy ===
Collaboration on homework assignments is encouraged. You may consult outside reference materials, other students, the TA, or the instructor. Use of solutions from previous years in the course or from other external sources is not allowed. All solutions that are handed should reﬂect your understanding of the subject matter at the time of writing.

No collaboration is allowed on the ﬁnal exam.

== Old Announcements ==

ACM 101/AM 125b/CDS 140a, Winter 2011

2011-02-07T08:50:37Z

Genti: /* Lecture Schedule */

{| width=100%
|-
| colspan=2 align=center |
Differential Equations and Dynamical Systems__NOTOC__
|- valign=top
| width=50% |
'''Instructors'''
* Richard Murray (CDS/BE)
* Gentian Buzi (CDS)
* Lectures: Tu/Th, 9-10:30, 105 ANB
| width=50% |
'''Teaching Assistants'''
* Molei Tao (CDS)
* Zhaoqian (Steven) Xie (CDS)
* Office hours: Mon 2-3pm, 314 ANB; Wed 12-2pm, 107 ANB
|}

=== Course Description ===
Analytical methods for the formulation and solution of initial value problems for ordinary differential equations. Basics in topics in dynamical systems in Euclidean space, including equilibria, stability, phase diagrams, Lyapunov functions, periodic solutions, Poincaré-Bendixon theory, Poincaré maps. Introduction to simple bifurcations, including Hopf bifurcations, invariant and center manifolds.

===Announcements ===
* 01 Feb 2011: [[Media:cds140a-wi11-hw5-newstyle.pdf|HW #5]] is now posted; due 10 Feb 2011
* 25 Jan 2011: [[CDS 140a Winter 2011 Homework 4|HW #4]] is now posted; due 3 Feb 2011
* 18 Jan 2011: [[CDS 140a Winter 2011 Homework 3|HW #3]] is now posted; due 27 Jan 2011
* 11 Jan 2011: [[CDS 140a Winter 2011 Homework 2|HW #2]] is now posted; due 20 Jan 2011
* 6 Jan 2011: Office hours for HW #1 will be on 10 Jan (Mon) from 4-6 pm in 235 ANB; office hours for future weeks will be on Wednesdays from 12-2 in 235 ANB
* 6 Jan 2011: Course ombuds: Jeff Amelang and Matanya Horowitz
* 3 Jan 2011: [[CDS 140a Winter 2011 Homework 1|HW #1]] is now posted; due 11 Jan 2011
* 14 Nov 2010: web page creation

=== Lecture Schedule ===

{| width=100% border=1 cellspacing=0 cellpadding=5
|-
| '''Week'''
| '''Date'''
| '''Topic'''
| '''Reading'''
| '''Homework'''
|- valign=top
|- valign=top
| 1
| 4 Jan 6 Jan
| Linear Differential Equations I
* Course overview and administration
* Linear differential equations
* Matrix exponential, diagonalization
* Stable and unstable spaces
* Planar systems, behavior of solutions
|
Perko, 1.1-1.6 
Optional:
* J&S, Ch 1 
* J&S, 2.1-2.5
| [[CDS 140a Winter 2011 Homework 1|HW 1]]
|- valign=top
| 2
| 11 Jan 13 Jan
| Linear Differential Equations II
* S + N decomposition, Jordan form
* Stability theory
* Linear systems with inputs (nonhomogeneous systems)
* Boundary value problems
| Perko, 1.7-1.10 + notes
| [[CDS 140a Winter 2011 Homework 2|HW 2]]
|- valign=top
| 3
| 18 Jan 20 Jan
| Nonlinear differential equations
* Existence and uniqueness
* Flow of a differential equation
* Linearization
| Perko, 2.1-2.6
| [[CDS 140a Winter 2011 Homework 3|HW 3]]
|- valign=top
| 4
| 25 Jan 27 Jan
| Behavior of differential equations
* Stable and unstable manifolds
* Stability of equilibrium points
| Perko, 2.7-2.10
* [[Media:cds140a-wi11-Week4Notes.pdf|Some notes]]
| | [[CDS 140a Winter 2011 Homework 4|HW 4]]
|- valign=top
| 5
| 1 Feb* 3 Feb*
| Non-hyperbolic differential equations
* Lyapunov functions
* Center manifold theorem
| Perko, 2.11-2.13
* [[Media:cds140a-wi11-Week5Notes.pdf|Notes on Lyapunov]]
* [[Media:cds140a-wi11-Week5NotesCMT.pdf|Notes on Center Manifold]]
| [[Media:cds140a-wi11-hw5-newstyle.pdf|HW 5]]
|- valign=top
| 6
| 8 Feb* 10 Feb
| Hamiltonian systems
* Gradient and Hamiltonian systems
* Energy based stability methods
* Applications
| Perko 2.14 + notes
| [[Media:cds140a-wi11-hw6.pdf|HW 6]] (draft version)
|- valign=top
| 7
| 15 Feb 17 Feb
| Limit cycles
* Limit sets and attractors
* Periodic orbits and limit cycles
* Poincare' map
* Bendixson criterion for limit cycles in the plane
| Perko, 3.2-3.4, 3.9
| 
|- valign=top
| 8
| 22 Feb 24 Feb
| Bifurcations
* Structural stability
* Bifurcation of equilibrium points
* Hopf bifurcation
| Perko 4.1-4.4
| 
|- valign=top
| 9
| 1 Mar 3 Mar
| Advanced topics
* Higher co-dimension bifurcations
* Homoclinic bifurcation
| Perko, 4-3, 4.5-4.8, notes
| 
|- valign=top
| 10
| 8 Mar 
| Course review
| 
| 
|}

=== Textbook ===

The primary text for the course (available via the online bookstore) is
{|
|- valign=top
| align=right |  [Perko] 
| L. Perko, Differential Equations and Dynamical Systems, Third Edition. Springer, 2006.
|}

The following additional texts may be useful for some students (on reserve in SFL):
{|
|- valign=top
| align=right |  [J&S] 
| D. Jordan and P. Smith, Nonlinear Ordinary Differential Equations: An Introduction for Scientists and Engineers, Fourth Edition. Oxford University Press, 2007.
|}

=== Grading ===
The ﬁnal grade will be based on homework and a ﬁnal exam:
* Homework (75%) - There will be 9 one-week problem sets, due in class approximately one week after they are assigned. Late homework will not be accepted without prior permission from the instructor.
* Final exam (25%) - The ﬁnal will be handed out the last day of class and is due back at the end of ﬁnals week. Open book, time limit to be decided (likely N hours over a 4-8N hour period).

The lowest homework score you receive will be dropped in computing your homework average. In addition, if your score on the ﬁnal is higher than the weighted average of your homework and ﬁnal, your ﬁnal will be used to determine your course grade.

=== Collaboration Policy ===
Collaboration on homework assignments is encouraged. You may consult outside reference materials, other students, the TA, or the instructor. Use of solutions from previous years in the course or from other external sources is not allowed. All solutions that are handed should reﬂect your understanding of the subject matter at the time of writing.

No collaboration is allowed on the ﬁnal exam.

== Old Announcements ==

File:Cds140a-wi11-hw6.pdf

2011-02-07T08:49:29Z

Genti:

ACM 101/AM 125b/CDS 140a, Winter 2011

2011-02-03T19:14:39Z

Genti: /* Lecture Schedule */

{| width=100%
|-
| colspan=2 align=center |
Differential Equations and Dynamical Systems__NOTOC__
|- valign=top
| width=50% |
'''Instructors'''
* Richard Murray (CDS/BE)
* Gentian Buzi (CDS)
* Lectures: Tu/Th, 9-10:30, 105 ANB
| width=50% |
'''Teaching Assistants'''
* Molei Tao (CDS)
* Zhaoqian (Steven) Xie (CDS)
* Office hours: Mon 2-3pm, 314 ANB; Wed 12-2pm, 107 ANB
|}

=== Course Description ===
Analytical methods for the formulation and solution of initial value problems for ordinary differential equations. Basics in topics in dynamical systems in Euclidean space, including equilibria, stability, phase diagrams, Lyapunov functions, periodic solutions, Poincaré-Bendixon theory, Poincaré maps. Introduction to simple bifurcations, including Hopf bifurcations, invariant and center manifolds.

===Announcements ===
* 01 Feb 2011: [[Media:cds140a-wi11-hw5-newstyle.pdf|HW #5]] is now posted; due 10 Feb 2011
* 25 Jan 2011: [[CDS 140a Winter 2011 Homework 4|HW #4]] is now posted; due 3 Feb 2011
* 18 Jan 2011: [[CDS 140a Winter 2011 Homework 3|HW #3]] is now posted; due 27 Jan 2011
* 11 Jan 2011: [[CDS 140a Winter 2011 Homework 2|HW #2]] is now posted; due 20 Jan 2011
* 6 Jan 2011: Office hours for HW #1 will be on 10 Jan (Mon) from 4-6 pm in 235 ANB; office hours for future weeks will be on Wednesdays from 12-2 in 235 ANB
* 6 Jan 2011: Course ombuds: Jeff Amelang and Matanya Horowitz
* 3 Jan 2011: [[CDS 140a Winter 2011 Homework 1|HW #1]] is now posted; due 11 Jan 2011
* 14 Nov 2010: web page creation

=== Lecture Schedule ===

{| width=100% border=1 cellspacing=0 cellpadding=5
|-
| '''Week'''
| '''Date'''
| '''Topic'''
| '''Reading'''
| '''Homework'''
|- valign=top
|- valign=top
| 1
| 4 Jan 6 Jan
| Linear Differential Equations I
* Course overview and administration
* Linear differential equations
* Matrix exponential, diagonalization
* Stable and unstable spaces
* Planar systems, behavior of solutions
|
Perko, 1.1-1.6 
Optional:
* J&S, Ch 1 
* J&S, 2.1-2.5
| [[CDS 140a Winter 2011 Homework 1|HW 1]]
|- valign=top
| 2
| 11 Jan 13 Jan
| Linear Differential Equations II
* S + N decomposition, Jordan form
* Stability theory
* Linear systems with inputs (nonhomogeneous systems)
* Boundary value problems
| Perko, 1.7-1.10 + notes
| [[CDS 140a Winter 2011 Homework 2|HW 2]]
|- valign=top
| 3
| 18 Jan 20 Jan
| Nonlinear differential equations
* Existence and uniqueness
* Flow of a differential equation
* Linearization
| Perko, 2.1-2.6
| [[CDS 140a Winter 2011 Homework 3|HW 3]]
|- valign=top
| 4
| 25 Jan 27 Jan
| Behavior of differential equations
* Stable and unstable manifolds
* Stability of equilibrium points
| Perko, 2.7-2.10
* [[Media:cds140a-wi11-Week4Notes.pdf|Some notes]]
| | [[CDS 140a Winter 2011 Homework 4|HW 4]]
|- valign=top
| 5
| 1 Feb* 3 Feb*
| Non-hyperbolic differential equations
* Lyapunov functions
* Center manifold theorem
| Perko, 2.11-2.13
* [[Media:cds140a-wi11-Week5Notes.pdf|Notes on Lyapunov]]
* [[Media:cds140a-wi11-Week5NotesCMT.pdf|Notes on Center Manifold]]
| [[Media:cds140a-wi11-hw5-newstyle.pdf|HW 5]]
|- valign=top
| 6
| 8 Feb* 10 Feb
| Hamiltonian systems
* Gradient and Hamiltonian systems
* Energy based stability methods
* Applications
| Perko 2.14 + notes
| 
|- valign=top
| 7
| 15 Feb 17 Feb
| Limit cycles
* Limit sets and attractors
* Periodic orbits and limit cycles
* Poincare' map
* Bendixson criterion for limit cycles in the plane
| Perko, 3.2-3.4, 3.9
| 
|- valign=top
| 8
| 22 Feb 24 Feb
| Bifurcations
* Structural stability
* Bifurcation of equilibrium points
* Hopf bifurcation
| Perko 4.1-4.4
| 
|- valign=top
| 9
| 1 Mar 3 Mar
| Advanced topics
* Higher co-dimension bifurcations
* Homoclinic bifurcation
| Perko, 4-3, 4.5-4.8, notes
| 
|- valign=top
| 10
| 8 Mar 
| Course review
| 
| 
|}

=== Textbook ===

The primary text for the course (available via the online bookstore) is
{|
|- valign=top
| align=right |  [Perko] 
| L. Perko, Differential Equations and Dynamical Systems, Third Edition. Springer, 2006.
|}

The following additional texts may be useful for some students (on reserve in SFL):
{|
|- valign=top
| align=right |  [J&S] 
| D. Jordan and P. Smith, Nonlinear Ordinary Differential Equations: An Introduction for Scientists and Engineers, Fourth Edition. Oxford University Press, 2007.
|}

=== Grading ===
The ﬁnal grade will be based on homework and a ﬁnal exam:
* Homework (75%) - There will be 9 one-week problem sets, due in class approximately one week after they are assigned. Late homework will not be accepted without prior permission from the instructor.
* Final exam (25%) - The ﬁnal will be handed out the last day of class and is due back at the end of ﬁnals week. Open book, time limit to be decided (likely N hours over a 4-8N hour period).

The lowest homework score you receive will be dropped in computing your homework average. In addition, if your score on the ﬁnal is higher than the weighted average of your homework and ﬁnal, your ﬁnal will be used to determine your course grade.

=== Collaboration Policy ===
Collaboration on homework assignments is encouraged. You may consult outside reference materials, other students, the TA, or the instructor. Use of solutions from previous years in the course or from other external sources is not allowed. All solutions that are handed should reﬂect your understanding of the subject matter at the time of writing.

No collaboration is allowed on the ﬁnal exam.

== Old Announcements ==

File:Cds140a-wi11-Week5NotesCMT.pdf

2011-02-03T19:12:51Z

Genti:

ACM 101/AM 125b/CDS 140a, Winter 2011

2011-02-01T22:25:59Z

Genti:

{| width=100%
|-
| colspan=2 align=center |
Differential Equations and Dynamical Systems__NOTOC__
|- valign=top
| width=50% |
'''Instructors'''
* Richard Murray (CDS/BE)
* Gentian Buzi (CDS)
* Lectures: Tu/Th, 9-10:30, 105 ANB
| width=50% |
'''Teaching Assistants'''
* Molei Tao (CDS)
* Zhaoqian (Steven) Xie (CDS)
* Office hours: Mon 2-3pm, 314 ANB; Wed 12-2pm, 107 ANB
|}

=== Course Description ===
Analytical methods for the formulation and solution of initial value problems for ordinary differential equations. Basics in topics in dynamical systems in Euclidean space, including equilibria, stability, phase diagrams, Lyapunov functions, periodic solutions, Poincaré-Bendixon theory, Poincaré maps. Introduction to simple bifurcations, including Hopf bifurcations, invariant and center manifolds.

===Announcements ===
* 01 Feb 2011: [[Media:cds140a-wi11-hw5-newstyle.pdf|HW #5]] is now posted; due 10 Feb 2011
* 25 Jan 2011: [[CDS 140a Winter 2011 Homework 4|HW #4]] is now posted; due 3 Feb 2011
* 18 Jan 2011: [[CDS 140a Winter 2011 Homework 3|HW #3]] is now posted; due 27 Jan 2011
* 11 Jan 2011: [[CDS 140a Winter 2011 Homework 2|HW #2]] is now posted; due 20 Jan 2011
* 6 Jan 2011: Office hours for HW #1 will be on 10 Jan (Mon) from 4-6 pm in 235 ANB; office hours for future weeks will be on Wednesdays from 12-2 in 235 ANB
* 6 Jan 2011: Course ombuds: Jeff Amelang and Matanya Horowitz
* 3 Jan 2011: [[CDS 140a Winter 2011 Homework 1|HW #1]] is now posted; due 11 Jan 2011
* 14 Nov 2010: web page creation

=== Lecture Schedule ===

{| width=100% border=1 cellspacing=0 cellpadding=5
|-
| '''Week'''
| '''Date'''
| '''Topic'''
| '''Reading'''
| '''Homework'''
|- valign=top
|- valign=top
| 1
| 4 Jan 6 Jan
| Linear Differential Equations I
* Course overview and administration
* Linear differential equations
* Matrix exponential, diagonalization
* Stable and unstable spaces
* Planar systems, behavior of solutions
|
Perko, 1.1-1.6 
Optional:
* J&S, Ch 1 
* J&S, 2.1-2.5
| [[CDS 140a Winter 2011 Homework 1|HW 1]]
|- valign=top
| 2
| 11 Jan 13 Jan
| Linear Differential Equations II
* S + N decomposition, Jordan form
* Stability theory
* Linear systems with inputs (nonhomogeneous systems)
* Boundary value problems
| Perko, 1.7-1.10 + notes
| [[CDS 140a Winter 2011 Homework 2|HW 2]]
|- valign=top
| 3
| 18 Jan 20 Jan
| Nonlinear differential equations
* Existence and uniqueness
* Flow of a differential equation
* Linearization
| Perko, 2.1-2.6
| [[CDS 140a Winter 2011 Homework 3|HW 3]]
|- valign=top
| 4
| 25 Jan 27 Jan
| Behavior of differential equations
* Stable and unstable manifolds
* Stability and Lyapunov functions
| Perko, 2.7-2.10
* [[Media:cds140a-wi11-Week4Notes.pdf|Some notes]]
| | [[CDS 140a Winter 2011 Homework 4|HW 4]]
|- valign=top
| 5
| 1 Feb* 3 Feb*
| Non-hyperbolic differential equations
* Lyapunov functions
* Center manifold theorem
| Perko, 2.11-2.13
* [[Media:cds140a-wi11-Week5Notes.pdf|Notes on Lyapunov]]
| [[Media:cds140a-wi11-hw5-newstyle.pdf|HW 5]]
|- valign=top
| 6
| 8 Feb* 10 Feb
| Hamiltonian systems
* Gradient and Hamiltonian systems
* Energy based stability methods
* Applications
| Perko 2.14 + notes
| 
|- valign=top
| 7
| 15 Feb 17 Feb
| Limit cycles
* Limit sets and attractors
* Periodic orbits and limit cycles
* Poincare' map
* Bendixson criterion for limit cycles in the plane
| Perko, 3.2-3.4, 3.9
| 
|- valign=top
| 8
| 22 Feb 24 Feb
| Bifurcations
* Structural stability
* Bifurcation of equilibrium points
* Hopf bifurcation
| Perko 4.1-4.4
| 
|- valign=top
| 9
| 1 Mar 3 Mar
| Advanced topics
* Higher co-dimension bifurcations
* Homoclinic bifurcation
| Perko, 4-3, 4.5-4.8, notes
| 
|- valign=top
| 10
| 8 Mar 
| Course review
| 
| 
|}

=== Textbook ===

The primary text for the course (available via the online bookstore) is
{|
|- valign=top
| align=right |  [Perko] 
| L. Perko, Differential Equations and Dynamical Systems, Third Edition. Springer, 2006.
|}

The following additional texts may be useful for some students (on reserve in SFL):
{|
|- valign=top
| align=right |  [J&S] 
| D. Jordan and P. Smith, Nonlinear Ordinary Differential Equations: An Introduction for Scientists and Engineers, Fourth Edition. Oxford University Press, 2007.
|}

=== Grading ===
The ﬁnal grade will be based on homework and a ﬁnal exam:
* Homework (75%) - There will be 9 one-week problem sets, due in class approximately one week after they are assigned. Late homework will not be accepted without prior permission from the instructor.
* Final exam (25%) - The ﬁnal will be handed out the last day of class and is due back at the end of ﬁnals week. Open book, time limit to be decided (likely N hours over a 4-8N hour period).

The lowest homework score you receive will be dropped in computing your homework average. In addition, if your score on the ﬁnal is higher than the weighted average of your homework and ﬁnal, your ﬁnal will be used to determine your course grade.

=== Collaboration Policy ===
Collaboration on homework assignments is encouraged. You may consult outside reference materials, other students, the TA, or the instructor. Use of solutions from previous years in the course or from other external sources is not allowed. All solutions that are handed should reﬂect your understanding of the subject matter at the time of writing.

No collaboration is allowed on the ﬁnal exam.

== Old Announcements ==

ACM 101/AM 125b/CDS 140a, Winter 2011

2011-02-01T22:21:54Z

Genti: /* Lecture Schedule */

{| width=100%
|-
| colspan=2 align=center |
Differential Equations and Dynamical Systems__NOTOC__
|- valign=top
| width=50% |
'''Instructors'''
* Richard Murray (CDS/BE)
* Gentian Buzi (CDS)
* Lectures: Tu/Th, 9-10:30, 105 ANB
| width=50% |
'''Teaching Assistants'''
* Molei Tao (CDS)
* Zhaoqian (Steven) Xie (CDS)
* Office hours: Mon 2-3pm, 314 ANB; Wed 12-2pm, 107 ANB
|}

=== Course Description ===
Analytical methods for the formulation and solution of initial value problems for ordinary differential equations. Basics in topics in dynamical systems in Euclidean space, including equilibria, stability, phase diagrams, Lyapunov functions, periodic solutions, Poincaré-Bendixon theory, Poincaré maps. Introduction to simple bifurcations, including Hopf bifurcations, invariant and center manifolds.

===Announcements ===
* 25 Jan 2011: [[CDS 140a Winter 2011 Homework 4|HW #4]] is now posted; due 3 Feb 2011
* 18 Jan 2011: [[CDS 140a Winter 2011 Homework 3|HW #3]] is now posted; due 27 Jan 2011
* 11 Jan 2011: [[CDS 140a Winter 2011 Homework 2|HW #2]] is now posted; due 20 Jan 2011
* 6 Jan 2011: Office hours for HW #1 will be on 10 Jan (Mon) from 4-6 pm in 235 ANB; office hours for future weeks will be on Wednesdays from 12-2 in 235 ANB
* 6 Jan 2011: Course ombuds: Jeff Amelang and Matanya Horowitz
* 3 Jan 2011: [[CDS 140a Winter 2011 Homework 1|HW #1]] is now posted; due 11 Jan 2011
* 14 Nov 2010: web page creation

=== Lecture Schedule ===

{| width=100% border=1 cellspacing=0 cellpadding=5
|-
| '''Week'''
| '''Date'''
| '''Topic'''
| '''Reading'''
| '''Homework'''
|- valign=top
|- valign=top
| 1
| 4 Jan 6 Jan
| Linear Differential Equations I
* Course overview and administration
* Linear differential equations
* Matrix exponential, diagonalization
* Stable and unstable spaces
* Planar systems, behavior of solutions
|
Perko, 1.1-1.6 
Optional:
* J&S, Ch 1 
* J&S, 2.1-2.5
| [[CDS 140a Winter 2011 Homework 1|HW 1]]
|- valign=top
| 2
| 11 Jan 13 Jan
| Linear Differential Equations II
* S + N decomposition, Jordan form
* Stability theory
* Linear systems with inputs (nonhomogeneous systems)
* Boundary value problems
| Perko, 1.7-1.10 + notes
| [[CDS 140a Winter 2011 Homework 2|HW 2]]
|- valign=top
| 3
| 18 Jan 20 Jan
| Nonlinear differential equations
* Existence and uniqueness
* Flow of a differential equation
* Linearization
| Perko, 2.1-2.6
| [[CDS 140a Winter 2011 Homework 3|HW 3]]
|- valign=top
| 4
| 25 Jan 27 Jan
| Behavior of differential equations
* Stable and unstable manifolds
* Stability and Lyapunov functions
| Perko, 2.7-2.10
* [[Media:cds140a-wi11-Week4Notes.pdf|Some notes]]
| | [[CDS 140a Winter 2011 Homework 4|HW 4]]
|- valign=top
| 5
| 1 Feb* 3 Feb*
| Non-hyperbolic differential equations
* Lyapunov functions
* Center manifold theorem
| Perko, 2.11-2.13
* [[Media:cds140a-wi11-Week5Notes.pdf|Notes on Lyapunov]]
| [[Media:cds140a-wi11-hw5-newstyle.pdf|HW 5]]
|- valign=top
| 6
| 8 Feb* 10 Feb
| Hamiltonian systems
* Gradient and Hamiltonian systems
* Energy based stability methods
* Applications
| Perko 2.14 + notes
| 
|- valign=top
| 7
| 15 Feb 17 Feb
| Limit cycles
* Limit sets and attractors
* Periodic orbits and limit cycles
* Poincare' map
* Bendixson criterion for limit cycles in the plane
| Perko, 3.2-3.4, 3.9
| 
|- valign=top
| 8
| 22 Feb 24 Feb
| Bifurcations
* Structural stability
* Bifurcation of equilibrium points
* Hopf bifurcation
| Perko 4.1-4.4
| 
|- valign=top
| 9
| 1 Mar 3 Mar
| Advanced topics
* Higher co-dimension bifurcations
* Homoclinic bifurcation
| Perko, 4-3, 4.5-4.8, notes
| 
|- valign=top
| 10
| 8 Mar 
| Course review
| 
| 
|}

=== Textbook ===

The primary text for the course (available via the online bookstore) is
{|
|- valign=top
| align=right |  [Perko] 
| L. Perko, Differential Equations and Dynamical Systems, Third Edition. Springer, 2006.
|}

The following additional texts may be useful for some students (on reserve in SFL):
{|
|- valign=top
| align=right |  [J&S] 
| D. Jordan and P. Smith, Nonlinear Ordinary Differential Equations: An Introduction for Scientists and Engineers, Fourth Edition. Oxford University Press, 2007.
|}

=== Grading ===
The ﬁnal grade will be based on homework and a ﬁnal exam:
* Homework (75%) - There will be 9 one-week problem sets, due in class approximately one week after they are assigned. Late homework will not be accepted without prior permission from the instructor.
* Final exam (25%) - The ﬁnal will be handed out the last day of class and is due back at the end of ﬁnals week. Open book, time limit to be decided (likely N hours over a 4-8N hour period).

The lowest homework score you receive will be dropped in computing your homework average. In addition, if your score on the ﬁnal is higher than the weighted average of your homework and ﬁnal, your ﬁnal will be used to determine your course grade.

=== Collaboration Policy ===
Collaboration on homework assignments is encouraged. You may consult outside reference materials, other students, the TA, or the instructor. Use of solutions from previous years in the course or from other external sources is not allowed. All solutions that are handed should reﬂect your understanding of the subject matter at the time of writing.

No collaboration is allowed on the ﬁnal exam.

== Old Announcements ==

File:Cds140a-wi11-Week5Notes.pdf

2011-02-01T22:20:51Z

Genti:

ACM 101/AM 125b/CDS 140a, Winter 2011

2011-01-31T19:06:48Z

Genti:

{| width=100%
|-
| colspan=2 align=center |
Differential Equations and Dynamical Systems__NOTOC__
|- valign=top
| width=50% |
'''Instructors'''
* Richard Murray (CDS/BE)
* Gentian Buzi (CDS)
* Lectures: Tu/Th, 9-10:30, 105 ANB
| width=50% |
'''Teaching Assistants'''
* Molei Tao (CDS)
* Zhaoqian (Steven) Xie (CDS)
* Office hours: Mon 2-3pm, 314 ANB; Wed 12-2pm, 107 ANB
|}

=== Course Description ===
Analytical methods for the formulation and solution of initial value problems for ordinary differential equations. Basics in topics in dynamical systems in Euclidean space, including equilibria, stability, phase diagrams, Lyapunov functions, periodic solutions, Poincaré-Bendixon theory, Poincaré maps. Introduction to simple bifurcations, including Hopf bifurcations, invariant and center manifolds.

===Announcements ===
* 25 Jan 2011: [[CDS 140a Winter 2011 Homework 4|HW #4]] is now posted; due 3 Feb 2011
* 18 Jan 2011: [[CDS 140a Winter 2011 Homework 3|HW #3]] is now posted; due 27 Jan 2011
* 11 Jan 2011: [[CDS 140a Winter 2011 Homework 2|HW #2]] is now posted; due 20 Jan 2011
* 6 Jan 2011: Office hours for HW #1 will be on 10 Jan (Mon) from 4-6 pm in 235 ANB; office hours for future weeks will be on Wednesdays from 12-2 in 235 ANB
* 6 Jan 2011: Course ombuds: Jeff Amelang and Matanya Horowitz
* 3 Jan 2011: [[CDS 140a Winter 2011 Homework 1|HW #1]] is now posted; due 11 Jan 2011
* 14 Nov 2010: web page creation

=== Lecture Schedule ===

{| width=100% border=1 cellspacing=0 cellpadding=5
|-
| '''Week'''
| '''Date'''
| '''Topic'''
| '''Reading'''
| '''Homework'''
|- valign=top
|- valign=top
| 1
| 4 Jan 6 Jan
| Linear Differential Equations I
* Course overview and administration
* Linear differential equations
* Matrix exponential, diagonalization
* Stable and unstable spaces
* Planar systems, behavior of solutions
|
Perko, 1.1-1.6 
Optional:
* J&S, Ch 1 
* J&S, 2.1-2.5
| [[CDS 140a Winter 2011 Homework 1|HW 1]]
|- valign=top
| 2
| 11 Jan 13 Jan
| Linear Differential Equations II
* S + N decomposition, Jordan form
* Stability theory
* Linear systems with inputs (nonhomogeneous systems)
* Boundary value problems
| Perko, 1.7-1.10 + notes
| [[CDS 140a Winter 2011 Homework 2|HW 2]]
|- valign=top
| 3
| 18 Jan 20 Jan
| Nonlinear differential equations
* Existence and uniqueness
* Flow of a differential equation
* Linearization
| Perko, 2.1-2.6
| [[CDS 140a Winter 2011 Homework 3|HW 3]]
|- valign=top
| 4
| 25 Jan 27 Jan
| Behavior of differential equations
* Stable and unstable manifolds
* Stability and Lyapunov functions
| Perko, 2.7-2.10
* [[Media:cds140a-wi11-Week4Notes.pdf|Some notes]]
| | [[CDS 140a Winter 2011 Homework 4|HW 4]]
|- valign=top
| 5
| 1 Feb* 3 Feb*
| Non-hyperbolic differential equations
* Lyapunov functions
* Center manifold theorem
| Perko, 2.11-2.13
| [[Media:cds140a-wi11-hw5-newstyle.pdf|HW 5]] (Draft Version)
|- valign=top
| 6
| 8 Feb* 10 Feb
| Hamiltonian systems
* Gradient and Hamiltonian systems
* Energy based stability methods
* Applications
| Perko 2.14 + notes
| 
|- valign=top
| 7
| 15 Feb 17 Feb
| Limit cycles
* Limit sets and attractors
* Periodic orbits and limit cycles
* Poincare' map
* Bendixson criterion for limit cycles in the plane
| Perko, 3.2-3.4, 3.9
| 
|- valign=top
| 8
| 22 Feb 24 Feb
| Bifurcations
* Structural stability
* Bifurcation of equilibrium points
* Hopf bifurcation
| Perko 4.1-4.4
| 
|- valign=top
| 9
| 1 Mar 3 Mar
| Advanced topics
* Higher co-dimension bifurcations
* Homoclinic bifurcation
| Perko, 4-3, 4.5-4.8, notes
| 
|- valign=top
| 10
| 8 Mar 
| Course review
| 
| 
|}

=== Textbook ===

The primary text for the course (available via the online bookstore) is
{|
|- valign=top
| align=right |  [Perko] 
| L. Perko, Differential Equations and Dynamical Systems, Third Edition. Springer, 2006.
|}

The following additional texts may be useful for some students (on reserve in SFL):
{|
|- valign=top
| align=right |  [J&S] 
| D. Jordan and P. Smith, Nonlinear Ordinary Differential Equations: An Introduction for Scientists and Engineers, Fourth Edition. Oxford University Press, 2007.
|}

=== Grading ===
The ﬁnal grade will be based on homework and a ﬁnal exam:
* Homework (75%) - There will be 9 one-week problem sets, due in class approximately one week after they are assigned. Late homework will not be accepted without prior permission from the instructor.
* Final exam (25%) - The ﬁnal will be handed out the last day of class and is due back at the end of ﬁnals week. Open book, time limit to be decided (likely N hours over a 4-8N hour period).

The lowest homework score you receive will be dropped in computing your homework average. In addition, if your score on the ﬁnal is higher than the weighted average of your homework and ﬁnal, your ﬁnal will be used to determine your course grade.

=== Collaboration Policy ===
Collaboration on homework assignments is encouraged. You may consult outside reference materials, other students, the TA, or the instructor. Use of solutions from previous years in the course or from other external sources is not allowed. All solutions that are handed should reﬂect your understanding of the subject matter at the time of writing.

No collaboration is allowed on the ﬁnal exam.

== Old Announcements ==

ACM 101/AM 125b/CDS 140a, Winter 2011

2011-01-31T01:02:42Z

Genti: /* Lecture Schedule */

{| width=100%
|-
| colspan=2 align=center |
Differential Equations and Dynamical Systems__NOTOC__
|- valign=top
| width=50% |
'''Instructors'''
* Richard Murray (CDS/BE)
* Gentian Buzi (CDS)
* Lectures: Tu/Th, 9-10:30, 105 ANB
| width=50% |
'''Teaching Assistants'''
* Molei Tao (CDS)
* Zhaoqian (Steven) Xie (CDS)
* Office hours: Wednesday 12-1, 107 ANB
|}

=== Course Description ===
Analytical methods for the formulation and solution of initial value problems for ordinary differential equations. Basics in topics in dynamical systems in Euclidean space, including equilibria, stability, phase diagrams, Lyapunov functions, periodic solutions, Poincaré-Bendixon theory, Poincaré maps. Introduction to simple bifurcations, including Hopf bifurcations, invariant and center manifolds.

===Announcements ===
* 25 Jan 2011: [[CDS 140a Winter 2011 Homework 4|HW #4]] is now posted; due 3 Feb 2011
* 18 Jan 2011: [[CDS 140a Winter 2011 Homework 3|HW #3]] is now posted; due 27 Jan 2011
* 11 Jan 2011: [[CDS 140a Winter 2011 Homework 2|HW #2]] is now posted; due 20 Jan 2011
* 6 Jan 2011: Office hours for HW #1 will be on 10 Jan (Mon) from 4-6 pm in 235 ANB; office hours for future weeks will be on Wednesdays from 12-2 in 235 ANB
* 6 Jan 2011: Course ombuds: Jeff Amelang and Matanya Horowitz
* 3 Jan 2011: [[CDS 140a Winter 2011 Homework 1|HW #1]] is now posted; due 11 Jan 2011
* 14 Nov 2010: web page creation

=== Lecture Schedule ===

{| width=100% border=1 cellspacing=0 cellpadding=5
|-
| '''Week'''
| '''Date'''
| '''Topic'''
| '''Reading'''
| '''Homework'''
|- valign=top
|- valign=top
| 1
| 4 Jan 6 Jan
| Linear Differential Equations I
* Course overview and administration
* Linear differential equations
* Matrix exponential, diagonalization
* Stable and unstable spaces
* Planar systems, behavior of solutions
|
Perko, 1.1-1.6 
Optional:
* J&S, Ch 1 
* J&S, 2.1-2.5
| [[CDS 140a Winter 2011 Homework 1|HW 1]]
|- valign=top
| 2
| 11 Jan 13 Jan
| Linear Differential Equations II
* S + N decomposition, Jordan form
* Stability theory
* Linear systems with inputs (nonhomogeneous systems)
* Boundary value problems
| Perko, 1.7-1.10 + notes
| [[CDS 140a Winter 2011 Homework 2|HW 2]]
|- valign=top
| 3
| 18 Jan 20 Jan
| Nonlinear differential equations
* Existence and uniqueness
* Flow of a differential equation
* Linearization
| Perko, 2.1-2.6
| [[CDS 140a Winter 2011 Homework 3|HW 3]]
|- valign=top
| 4
| 25 Jan 27 Jan
| Behavior of differential equations
* Stable and unstable manifolds
* Stability and Lyapunov functions
| Perko, 2.7-2.10
* [[Media:cds140a-wi11-Week4Notes.pdf|Some notes]]
| | [[CDS 140a Winter 2011 Homework 4|HW 4]]
|- valign=top
| 5
| 1 Feb* 3 Feb*
| Non-hyperbolic differential equations
* Lyapunov functions
* Center manifold theorem
| Perko, 2.11-2.13
| [[Media:cds140a-wi11-hw5-newstyle.pdf|HW 5]] (Draft Version)
|- valign=top
| 6
| 8 Feb* 10 Feb
| Hamiltonian systems
* Gradient and Hamiltonian systems
* Energy based stability methods
* Applications
| Perko 2.14 + notes
| 
|- valign=top
| 7
| 15 Feb 17 Feb
| Limit cycles
* Limit sets and attractors
* Periodic orbits and limit cycles
* Poincare' map
* Bendixson criterion for limit cycles in the plane
| Perko, 3.2-3.4, 3.9
| 
|- valign=top
| 8
| 22 Feb 24 Feb
| Bifurcations
* Structural stability
* Bifurcation of equilibrium points
* Hopf bifurcation
| Perko 4.1-4.4
| 
|- valign=top
| 9
| 1 Mar 3 Mar
| Advanced topics
* Higher co-dimension bifurcations
* Homoclinic bifurcation
| Perko, 4-3, 4.5-4.8, notes
| 
|- valign=top
| 10
| 8 Mar 
| Course review
| 
| 
|}

=== Textbook ===

The primary text for the course (available via the online bookstore) is
{|
|- valign=top
| align=right |  [Perko] 
| L. Perko, Differential Equations and Dynamical Systems, Third Edition. Springer, 2006.
|}

The following additional texts may be useful for some students (on reserve in SFL):
{|
|- valign=top
| align=right |  [J&S] 
| D. Jordan and P. Smith, Nonlinear Ordinary Differential Equations: An Introduction for Scientists and Engineers, Fourth Edition. Oxford University Press, 2007.
|}

=== Grading ===
The ﬁnal grade will be based on homework and a ﬁnal exam:
* Homework (75%) - There will be 9 one-week problem sets, due in class approximately one week after they are assigned. Late homework will not be accepted without prior permission from the instructor.
* Final exam (25%) - The ﬁnal will be handed out the last day of class and is due back at the end of ﬁnals week. Open book, time limit to be decided (likely N hours over a 4-8N hour period).

The lowest homework score you receive will be dropped in computing your homework average. In addition, if your score on the ﬁnal is higher than the weighted average of your homework and ﬁnal, your ﬁnal will be used to determine your course grade.

=== Collaboration Policy ===
Collaboration on homework assignments is encouraged. You may consult outside reference materials, other students, the TA, or the instructor. Use of solutions from previous years in the course or from other external sources is not allowed. All solutions that are handed should reﬂect your understanding of the subject matter at the time of writing.

No collaboration is allowed on the ﬁnal exam.

== Old Announcements ==

File:Cds140a-wi11-hw5-newstyle.pdf

2011-01-31T00:29:23Z

Genti: uploaded a new version of "File:Cds140a-wi11-hw5-newstyle.pdf"

ACM 101/AM 125b/CDS 140a, Winter 2011

2011-01-31T00:06:07Z

Genti: /* Lecture Schedule */

{| width=100%
|-
| colspan=2 align=center |
Differential Equations and Dynamical Systems__NOTOC__
|- valign=top
| width=50% |
'''Instructors'''
* Richard Murray (CDS/BE)
* Gentian Buzi (CDS)
* Lectures: Tu/Th, 9-10:30, 105 ANB
| width=50% |
'''Teaching Assistants'''
* Molei Tao (CDS)
* Zhaoqian (Steven) Xie (CDS)
* Office hours: Wednesday 12-1, 107 ANB
|}

=== Course Description ===
Analytical methods for the formulation and solution of initial value problems for ordinary differential equations. Basics in topics in dynamical systems in Euclidean space, including equilibria, stability, phase diagrams, Lyapunov functions, periodic solutions, Poincaré-Bendixon theory, Poincaré maps. Introduction to simple bifurcations, including Hopf bifurcations, invariant and center manifolds.

===Announcements ===
* 25 Jan 2011: [[CDS 140a Winter 2011 Homework 4|HW #4]] is now posted; due 3 Feb 2011
* 18 Jan 2011: [[CDS 140a Winter 2011 Homework 3|HW #3]] is now posted; due 27 Jan 2011
* 11 Jan 2011: [[CDS 140a Winter 2011 Homework 2|HW #2]] is now posted; due 20 Jan 2011
* 6 Jan 2011: Office hours for HW #1 will be on 10 Jan (Mon) from 4-6 pm in 235 ANB; office hours for future weeks will be on Wednesdays from 12-2 in 235 ANB
* 6 Jan 2011: Course ombuds: Jeff Amelang and Matanya Horowitz
* 3 Jan 2011: [[CDS 140a Winter 2011 Homework 1|HW #1]] is now posted; due 11 Jan 2011
* 14 Nov 2010: web page creation

=== Lecture Schedule ===

{| width=100% border=1 cellspacing=0 cellpadding=5
|-
| '''Week'''
| '''Date'''
| '''Topic'''
| '''Reading'''
| '''Homework'''
|- valign=top
|- valign=top
| 1
| 4 Jan 6 Jan
| Linear Differential Equations I
* Course overview and administration
* Linear differential equations
* Matrix exponential, diagonalization
* Stable and unstable spaces
* Planar systems, behavior of solutions
|
Perko, 1.1-1.6 
Optional:
* J&S, Ch 1 
* J&S, 2.1-2.5
| [[CDS 140a Winter 2011 Homework 1|HW 1]]
|- valign=top
| 2
| 11 Jan 13 Jan
| Linear Differential Equations II
* S + N decomposition, Jordan form
* Stability theory
* Linear systems with inputs (nonhomogeneous systems)
* Boundary value problems
| Perko, 1.7-1.10 + notes
| [[CDS 140a Winter 2011 Homework 2|HW 2]]
|- valign=top
| 3
| 18 Jan 20 Jan
| Nonlinear differential equations
* Existence and uniqueness
* Flow of a differential equation
* Linearization
| Perko, 2.1-2.6
| [[CDS 140a Winter 2011 Homework 3|HW 3]]
|- valign=top
| 4
| 25 Jan 27 Jan
| Behavior of differential equations
* Stable and unstable manifolds
* Stability and Lyapunov functions
| Perko, 2.7-2.10
* [[Media:cds140a-wi11-Week4Notes.pdf|Some notes]]
| | [[CDS 140a Winter 2011 Homework 4|HW 4]]
|- valign=top
| 5
| 1 Feb* 3 Feb*
| Non-hyperbolic differential equations
* Center manifold theorem
* Normal forms
| Perko, 2.11-2.13
| [[Media:cds140a-wi11-hw5-newstyle.pdf|HW 5]] (Draft Version)
|- valign=top
| 6
| 8 Feb* 10 Feb
| Hamiltonian systems
* Gradient and Hamiltonian systems
* Energy based stability methods
* Applications
| Perko 2.14 + notes
| 
|- valign=top
| 7
| 15 Feb 17 Feb
| Limit cycles
* Limit sets and attractors
* Periodic orbits and limit cycles
* Poincare' map
* Bendixson criterion for limit cycles in the plane
| Perko, 3.2-3.4, 3.9
| 
|- valign=top
| 8
| 22 Feb 24 Feb
| Bifurcations
* Structural stability
* Bifurcation of equilibrium points
* Hopf bifurcation
| Perko 4.1-4.4
| 
|- valign=top
| 9
| 1 Mar 3 Mar
| Advanced topics
* Higher co-dimension bifurcations
* Homoclinic bifurcation
| Perko, 4-3, 4.5-4.8, notes
| 
|- valign=top
| 10
| 8 Mar 
| Course review
| 
| 
|}

=== Textbook ===

The primary text for the course (available via the online bookstore) is
{|
|- valign=top
| align=right |  [Perko] 
| L. Perko, Differential Equations and Dynamical Systems, Third Edition. Springer, 2006.
|}

The following additional texts may be useful for some students (on reserve in SFL):
{|
|- valign=top
| align=right |  [J&S] 
| D. Jordan and P. Smith, Nonlinear Ordinary Differential Equations: An Introduction for Scientists and Engineers, Fourth Edition. Oxford University Press, 2007.
|}

=== Grading ===
The ﬁnal grade will be based on homework and a ﬁnal exam:
* Homework (75%) - There will be 9 one-week problem sets, due in class approximately one week after they are assigned. Late homework will not be accepted without prior permission from the instructor.
* Final exam (25%) - The ﬁnal will be handed out the last day of class and is due back at the end of ﬁnals week. Open book, time limit to be decided (likely N hours over a 4-8N hour period).

The lowest homework score you receive will be dropped in computing your homework average. In addition, if your score on the ﬁnal is higher than the weighted average of your homework and ﬁnal, your ﬁnal will be used to determine your course grade.

=== Collaboration Policy ===
Collaboration on homework assignments is encouraged. You may consult outside reference materials, other students, the TA, or the instructor. Use of solutions from previous years in the course or from other external sources is not allowed. All solutions that are handed should reﬂect your understanding of the subject matter at the time of writing.

No collaboration is allowed on the ﬁnal exam.

== Old Announcements ==

File:Cds140a-wi11-hw5-newstyle.pdf

2011-01-31T00:01:40Z

Genti:

CDS 140a Winter 2011 Homework 4

2011-01-30T19:53:24Z

Genti:

{{CDS homework
| instructor = G. Buzi, R. Murray
| course = ACM 101/AM 125a/CDS 140a
| semester = Winter 2011
| title = Problem Set #3
| issued = 22 Jan 2011 (Tue)
| due = 3 Feb 2011 (Thu)
}}

'''Note:''' In the upper left hand corner of the ''second'' page of your homework set, please put the number of hours that you spent on
this homework set (including reading).

'''Note:''' You can use Mathematica or similar software packages. However make sure you include all the steps in the solution write-up.

:1. '''Perko, Section 2.7, problem 1''' 
:2. '''Perko, Section 2.7, problem 2''' 
:3. '''Perko, Section 2.7, problem 3 ''' 
:4, 5. Choose any 2 of the following:
::* '''Perko, Section 2.7, problem 4'''
::* '''Perko, Section 2.7, problem 5'''
::* '''Perko, Section 2.7, problem 6'''
::* '''Perko, Section 2.8, problem 1'''
:6. '''Perko, Section 2.9, problem 2(a)(b)'''

CDS 140a Winter 2011 Homework 5

2011-01-30T19:52:24Z

Genti: Created page with '{{HW draft}} {{CDS homework | instructor = G. Buzi, R. Murray | course = ACM 101/AM 125a/CDS 140a | semester = Winter 2011 | title = Problem Set #3 | issued = 1 Feb 2011 (T…'

{{HW draft}}
{{CDS homework
| instructor = G. Buzi, R. Murray
| course = ACM 101/AM 125a/CDS 140a
| semester = Winter 2011
| title = Problem Set #3
| issued = 1 Feb 2011 (Tue)
| due = 10 Feb 2011 (Thu)
}}

'''Note:''' In the upper left hand corner of the ''second'' page of your homework set, please put the number of hours that you spent on
this homework set (including reading).

* [[Media:cds140a-wi11-hw5.pdf|Homework 5]]

File:Cds140a-wi11-hw5.pdf

2011-01-30T19:51:14Z

Genti:

ACM 101/AM 125b/CDS 140a, Winter 2011

2011-01-30T19:47:44Z

Genti:

{| width=100%
|-
| colspan=2 align=center |
Differential Equations and Dynamical Systems__NOTOC__
|- valign=top
| width=50% |
'''Instructors'''
* Richard Murray (CDS/BE)
* Gentian Buzi (CDS)
* Lectures: Tu/Th, 9-10:30, 105 ANB
| width=50% |
'''Teaching Assistants'''
* Molei Tao (CDS)
* Zhaoqian (Steven) Xie (CDS)
* Office hours: Wednesday 12-1, 107 ANB
|}

=== Course Description ===
Analytical methods for the formulation and solution of initial value problems for ordinary differential equations. Basics in topics in dynamical systems in Euclidean space, including equilibria, stability, phase diagrams, Lyapunov functions, periodic solutions, Poincaré-Bendixon theory, Poincaré maps. Introduction to simple bifurcations, including Hopf bifurcations, invariant and center manifolds.

===Announcements ===
* 25 Jan 2011: [[CDS 140a Winter 2011 Homework 4|HW #4]] is now posted; due 3 Feb 2011
* 18 Jan 2011: [[CDS 140a Winter 2011 Homework 3|HW #3]] is now posted; due 27 Jan 2011
* 11 Jan 2011: [[CDS 140a Winter 2011 Homework 2|HW #2]] is now posted; due 20 Jan 2011
* 6 Jan 2011: Office hours for HW #1 will be on 10 Jan (Mon) from 4-6 pm in 235 ANB; office hours for future weeks will be on Wednesdays from 12-2 in 235 ANB
* 6 Jan 2011: Course ombuds: Jeff Amelang and Matanya Horowitz
* 3 Jan 2011: [[CDS 140a Winter 2011 Homework 1|HW #1]] is now posted; due 11 Jan 2011
* 14 Nov 2010: web page creation

=== Lecture Schedule ===

{| width=100% border=1 cellspacing=0 cellpadding=5
|-
| '''Week'''
| '''Date'''
| '''Topic'''
| '''Reading'''
| '''Homework'''
|- valign=top
|- valign=top
| 1
| 4 Jan 6 Jan
| Linear Differential Equations I
* Course overview and administration
* Linear differential equations
* Matrix exponential, diagonalization
* Stable and unstable spaces
* Planar systems, behavior of solutions
|
Perko, 1.1-1.6 
Optional:
* J&S, Ch 1 
* J&S, 2.1-2.5
| [[CDS 140a Winter 2011 Homework 1|HW 1]]
|- valign=top
| 2
| 11 Jan 13 Jan
| Linear Differential Equations II
* S + N decomposition, Jordan form
* Stability theory
* Linear systems with inputs (nonhomogeneous systems)
* Boundary value problems
| Perko, 1.7-1.10 + notes
| [[CDS 140a Winter 2011 Homework 2|HW 2]]
|- valign=top
| 3
| 18 Jan 20 Jan
| Nonlinear differential equations
* Existence and uniqueness
* Flow of a differential equation
* Linearization
| Perko, 2.1-2.6
| [[CDS 140a Winter 2011 Homework 3|HW 3]]
|- valign=top
| 4
| 25 Jan 27 Jan
| Behavior of differential equations
* Stable and unstable manifolds
* Stability and Lyapunov functions
| Perko, 2.7-2.10
* [[Media:cds140a-wi11-Week4Notes.pdf|Some notes]]
| | [[CDS 140a Winter 2011 Homework 4|HW 4]]
|- valign=top
| 5
| 1 Feb* 3 Feb*
| Non-hyperbolic differential equations
* Center manifold theorem
* Normal forms
| Perko, 2.11-2.13
| [[CDS 140a Winter 2011 Homework 5|HW 5]]
|- valign=top
| 6
| 8 Feb* 10 Feb
| Hamiltonian systems
* Gradient and Hamiltonian systems
* Energy based stability methods
* Applications
| Perko 2.14 + notes
| 
|- valign=top
| 7
| 15 Feb 17 Feb
| Limit cycles
* Limit sets and attractors
* Periodic orbits and limit cycles
* Poincare' map
* Bendixson criterion for limit cycles in the plane
| Perko, 3.2-3.4, 3.9
| 
|- valign=top
| 8
| 22 Feb 24 Feb
| Bifurcations
* Structural stability
* Bifurcation of equilibrium points
* Hopf bifurcation
| Perko 4.1-4.4
| 
|- valign=top
| 9
| 1 Mar 3 Mar
| Advanced topics
* Higher co-dimension bifurcations
* Homoclinic bifurcation
| Perko, 4-3, 4.5-4.8, notes
| 
|- valign=top
| 10
| 8 Mar 
| Course review
| 
| 
|}

=== Textbook ===

The primary text for the course (available via the online bookstore) is
{|
|- valign=top
| align=right |  [Perko] 
| L. Perko, Differential Equations and Dynamical Systems, Third Edition. Springer, 2006.
|}

The following additional texts may be useful for some students (on reserve in SFL):
{|
|- valign=top
| align=right |  [J&S] 
| D. Jordan and P. Smith, Nonlinear Ordinary Differential Equations: An Introduction for Scientists and Engineers, Fourth Edition. Oxford University Press, 2007.
|}

=== Grading ===
The ﬁnal grade will be based on homework and a ﬁnal exam:
* Homework (75%) - There will be 9 one-week problem sets, due in class approximately one week after they are assigned. Late homework will not be accepted without prior permission from the instructor.
* Final exam (25%) - The ﬁnal will be handed out the last day of class and is due back at the end of ﬁnals week. Open book, time limit to be decided (likely N hours over a 4-8N hour period).

The lowest homework score you receive will be dropped in computing your homework average. In addition, if your score on the ﬁnal is higher than the weighted average of your homework and ﬁnal, your ﬁnal will be used to determine your course grade.

=== Collaboration Policy ===
Collaboration on homework assignments is encouraged. You may consult outside reference materials, other students, the TA, or the instructor. Use of solutions from previous years in the course or from other external sources is not allowed. All solutions that are handed should reﬂect your understanding of the subject matter at the time of writing.

No collaboration is allowed on the ﬁnal exam.

== Old Announcements ==

ACM 101/AM 125b/CDS 140a, Winter 2011

2011-01-27T20:41:45Z

Genti:

{| width=100%
|-
| colspan=2 align=center |
Differential Equations and Dynamical Systems__NOTOC__
|- valign=top
| width=50% |
'''Instructors'''
* Richard Murray (CDS/BE)
* Gentian Buzi (CDS)
* Lectures: Tu/Th, 9-10:30, 105 ANB
| width=50% |
'''Teaching Assistants'''
* Molei Tao (CDS)
* Zhaoqian (Steven) Xie (CDS)
* Office hours: Wednesday 12-1, 107 ANB
|}

=== Course Description ===
Analytical methods for the formulation and solution of initial value problems for ordinary differential equations. Basics in topics in dynamical systems in Euclidean space, including equilibria, stability, phase diagrams, Lyapunov functions, periodic solutions, Poincaré-Bendixon theory, Poincaré maps. Introduction to simple bifurcations, including Hopf bifurcations, invariant and center manifolds.

===Announcements ===
* 25 Jan 2011: [[CDS 140a Winter 2011 Homework 4|HW #4]] is now posted; due 3 Feb 2011
* 18 Jan 2011: [[CDS 140a Winter 2011 Homework 3|HW #3]] is now posted; due 27 Jan 2011
* 11 Jan 2011: [[CDS 140a Winter 2011 Homework 2|HW #2]] is now posted; due 20 Jan 2011
* 6 Jan 2011: Office hours for HW #1 will be on 10 Jan (Mon) from 4-6 pm in 235 ANB; office hours for future weeks will be on Wednesdays from 12-2 in 235 ANB
* 6 Jan 2011: Course ombuds: Jeff Amelang and Matanya Horowitz
* 3 Jan 2011: [[CDS 140a Winter 2011 Homework 1|HW #1]] is now posted; due 11 Jan 2011
* 14 Nov 2010: web page creation

=== Lecture Schedule ===

{| width=100% border=1 cellspacing=0 cellpadding=5
|-
| '''Week'''
| '''Date'''
| '''Topic'''
| '''Reading'''
| '''Homework'''
|- valign=top
|- valign=top
| 1
| 4 Jan 6 Jan
| Linear Differential Equations I
* Course overview and administration
* Linear differential equations
* Matrix exponential, diagonalization
* Stable and unstable spaces
* Planar systems, behavior of solutions
|
Perko, 1.1-1.6 
Optional:
* J&S, Ch 1 
* J&S, 2.1-2.5
| [[CDS 140a Winter 2011 Homework 1|HW 1]]
|- valign=top
| 2
| 11 Jan 13 Jan
| Linear Differential Equations II
* S + N decomposition, Jordan form
* Stability theory
* Linear systems with inputs (nonhomogeneous systems)
* Boundary value problems
| Perko, 1.7-1.10 + notes
| [[CDS 140a Winter 2011 Homework 2|HW 2]]
|- valign=top
| 3
| 18 Jan 20 Jan
| Nonlinear differential equations
* Existence and uniqueness
* Flow of a differential equation
* Linearization
| Perko, 2.1-2.6
| [[CDS 140a Winter 2011 Homework 3|HW 3]]
|- valign=top
| 4
| 25 Jan 27 Jan
| Behavior of differential equations
* Stable and unstable manifolds
* Stability and Lyapunov functions
| Perko, 2.7-2.10
* [[Media:cds140a-wi11-Week4Notes.pdf|Some notes]]
| | [[CDS 140a Winter 2011 Homework 4|HW 4]]
|- valign=top
| 5
| 1 Feb* 3 Feb*
| Non-hyperbolic differential equations
* Center manifold theorem
* Normal forms
| Perko, 2.11-2.13
| 
|- valign=top
| 6
| 8 Feb* 10 Feb
| Hamiltonian systems
* Gradient and Hamiltonian systems
* Energy based stability methods
* Applications
| Perko 2.14 + notes
| 
|- valign=top
| 7
| 15 Feb 17 Feb
| Limit cycles
* Limit sets and attractors
* Periodic orbits and limit cycles
* Poincare' map
* Bendixson criterion for limit cycles in the plane
| Perko, 3.2-3.4, 3.9
| 
|- valign=top
| 8
| 22 Feb 24 Feb
| Bifurcations
* Structural stability
* Bifurcation of equilibrium points
* Hopf bifurcation
| Perko 4.1-4.4
| 
|- valign=top
| 9
| 1 Mar 3 Mar
| Advanced topics
* Higher co-dimension bifurcations
* Homoclinic bifurcation
| Perko, 4-3, 4.5-4.8, notes
| 
|- valign=top
| 10
| 8 Mar 
| Course review
| 
| 
|}

=== Textbook ===

The primary text for the course (available via the online bookstore) is
{|
|- valign=top
| align=right |  [Perko] 
| L. Perko, Differential Equations and Dynamical Systems, Third Edition. Springer, 2006.
|}

The following additional texts may be useful for some students (on reserve in SFL):
{|
|- valign=top
| align=right |  [J&S] 
| D. Jordan and P. Smith, Nonlinear Ordinary Differential Equations: An Introduction for Scientists and Engineers, Fourth Edition. Oxford University Press, 2007.
|}

=== Grading ===
The ﬁnal grade will be based on homework and a ﬁnal exam:
* Homework (75%) - There will be 9 one-week problem sets, due in class approximately one week after they are assigned. Late homework will not be accepted without prior permission from the instructor.
* Final exam (25%) - The ﬁnal will be handed out the last day of class and is due back at the end of ﬁnals week. Open book, time limit to be decided (likely N hours over a 4-8N hour period).

The lowest homework score you receive will be dropped in computing your homework average. In addition, if your score on the ﬁnal is higher than the weighted average of your homework and ﬁnal, your ﬁnal will be used to determine your course grade.

=== Collaboration Policy ===
Collaboration on homework assignments is encouraged. You may consult outside reference materials, other students, the TA, or the instructor. Use of solutions from previous years in the course or from other external sources is not allowed. All solutions that are handed should reﬂect your understanding of the subject matter at the time of writing.

No collaboration is allowed on the ﬁnal exam.

== Old Announcements ==

File:Cds140a-wi11-Week4Notes.pdf

2011-01-27T20:40:12Z

Genti:

ACM 101/AM 125b/CDS 140a, Winter 2011

2011-01-26T08:08:03Z

Genti:

{| width=100%
|-
| colspan=2 align=center |
Differential Equations and Dynamical Systems__NOTOC__
|- valign=top
| width=50% |
'''Instructors'''
* Richard Murray (CDS/BE)
* Gentian Buzi (CDS)
* Lectures: Tu/Th, 9-10:30, 105 ANB
| width=50% |
'''Teaching Assistants'''
* Molei Tao (CDS)
* Zhaoqian (Steven) Xie (CDS)
* Office hours: Wednesday 12-1, 107 ANB
|}

=== Course Description ===
Analytical methods for the formulation and solution of initial value problems for ordinary differential equations. Basics in topics in dynamical systems in Euclidean space, including equilibria, stability, phase diagrams, Lyapunov functions, periodic solutions, Poincaré-Bendixon theory, Poincaré maps. Introduction to simple bifurcations, including Hopf bifurcations, invariant and center manifolds.

===Announcements ===
* 25 Jan 2011: [[CDS 140a Winter 2011 Homework 4|HW #4]] is now posted; due 3 Feb 2011
* 18 Jan 2011: [[CDS 140a Winter 2011 Homework 3|HW #3]] is now posted; due 27 Jan 2011
* 11 Jan 2011: [[CDS 140a Winter 2011 Homework 2|HW #2]] is now posted; due 20 Jan 2011
* 6 Jan 2011: Office hours for HW #1 will be on 10 Jan (Mon) from 4-6 pm in 235 ANB; office hours for future weeks will be on Wednesdays from 12-2 in 235 ANB
* 6 Jan 2011: Course ombuds: Jeff Amelang and Matanya Horowitz
* 3 Jan 2011: [[CDS 140a Winter 2011 Homework 1|HW #1]] is now posted; due 11 Jan 2011
* 14 Nov 2010: web page creation

=== Lecture Schedule ===

{| width=100% border=1 cellspacing=0 cellpadding=5
|-
| '''Week'''
| '''Date'''
| '''Topic'''
| '''Reading'''
| '''Homework'''
|- valign=top
|- valign=top
| 1
| 4 Jan 6 Jan
| Linear Differential Equations I
* Course overview and administration
* Linear differential equations
* Matrix exponential, diagonalization
* Stable and unstable spaces
* Planar systems, behavior of solutions
|
Perko, 1.1-1.6 
Optional:
* J&S, Ch 1 
* J&S, 2.1-2.5
| [[CDS 140a Winter 2011 Homework 1|HW 1]]
|- valign=top
| 2
| 11 Jan 13 Jan
| Linear Differential Equations II
* S + N decomposition, Jordan form
* Stability theory
* Linear systems with inputs (nonhomogeneous systems)
* Boundary value problems
| Perko, 1.7-1.10 + notes
| [[CDS 140a Winter 2011 Homework 2|HW 2]]
|- valign=top
| 3
| 18 Jan 20 Jan
| Nonlinear differential equations
* Existence and uniqueness
* Flow of a differential equation
* Linearization
| Perko, 2.1-2.6
| [[CDS 140a Winter 2011 Homework 3|HW 3]]
|- valign=top
| 4
| 25 Jan 27 Jan
| Behavior of differential equations
* Stable and unstable manifolds ([[Media:cds140a-wi11-stablemanifoldNotes2.pdf|Some notes]])
* Stability and Lyapunov functions
* Planar systems, phase diagrams
| Perko, 2.7-2.10
| | [[CDS 140a Winter 2011 Homework 4|HW 4]]
|- valign=top
| 5
| 1 Feb* 3 Feb*
| Non-hyperbolic differential equations
* Center manifold theorem
* Normal forms
| Perko, 2.11-2.13
| 
|- valign=top
| 6
| 8 Feb* 10 Feb
| Hamiltonian systems
* Gradient and Hamiltonian systems
* Energy based stability methods
* Applications
| Perko 2.14 + notes
| 
|- valign=top
| 7
| 15 Feb 17 Feb
| Limit cycles
* Limit sets and attractors
* Periodic orbits and limit cycles
* Poincare' map
* Bendixson criterion for limit cycles in the plane
| Perko, 3.2-3.4, 3.9
| 
|- valign=top
| 8
| 22 Feb 24 Feb
| Bifurcations
* Structural stability
* Bifurcation of equilibrium points
* Hopf bifurcation
| Perko 4.1-4.4
| 
|- valign=top
| 9
| 1 Mar 3 Mar
| Advanced topics
* Higher co-dimension bifurcations
* Homoclinic bifurcation
| Perko, 4-3, 4.5-4.8, notes
| 
|- valign=top
| 10
| 8 Mar 
| Course review
| 
| 
|}

=== Textbook ===

The primary text for the course (available via the online bookstore) is
{|
|- valign=top
| align=right |  [Perko] 
| L. Perko, Differential Equations and Dynamical Systems, Third Edition. Springer, 2006.
|}

The following additional texts may be useful for some students (on reserve in SFL):
{|
|- valign=top
| align=right |  [J&S] 
| D. Jordan and P. Smith, Nonlinear Ordinary Differential Equations: An Introduction for Scientists and Engineers, Fourth Edition. Oxford University Press, 2007.
|}

=== Grading ===
The ﬁnal grade will be based on homework and a ﬁnal exam:
* Homework (75%) - There will be 9 one-week problem sets, due in class approximately one week after they are assigned. Late homework will not be accepted without prior permission from the instructor.
* Final exam (25%) - The ﬁnal will be handed out the last day of class and is due back at the end of ﬁnals week. Open book, time limit to be decided (likely N hours over a 4-8N hour period).

The lowest homework score you receive will be dropped in computing your homework average. In addition, if your score on the ﬁnal is higher than the weighted average of your homework and ﬁnal, your ﬁnal will be used to determine your course grade.

=== Collaboration Policy ===
Collaboration on homework assignments is encouraged. You may consult outside reference materials, other students, the TA, or the instructor. Use of solutions from previous years in the course or from other external sources is not allowed. All solutions that are handed should reﬂect your understanding of the subject matter at the time of writing.

No collaboration is allowed on the ﬁnal exam.

== Old Announcements ==

CDS 140a Winter 2011 Homework 4

2011-01-26T08:06:51Z

Genti:

{{CDS homework
| instructor = G. Buzi, R. Murray
| course = ACM 101/AM 125a/CDS 140a
| semester = Winter 2011
| title = Problem Set #3
| issued = 15 Jan 2011 (Tue)
| due = 3 Feb 2011 (Thu)
}}

'''Note:''' In the upper left hand corner of the ''second'' page of your homework set, please put the number of hours that you spent on
this homework set (including reading).

'''Note:''' You can use Mathematica or similar software packages. However make sure you include all the steps in the solution write-up.

:1. '''Perko, Section 2.7, problem 1''' 
:2. '''Perko, Section 2.7, problem 2''' 
:3. '''Perko, Section 2.7, problem 3 ''' 
:4, 5. Choose any 2 of the following:
::* '''Perko, Section 2.7, problem 4'''
::* '''Perko, Section 2.7, problem 5'''
::* '''Perko, Section 2.7, problem 6'''
::* '''Perko, Section 2.8, problem 1'''
:6. '''Perko, Section 2.9, problem 2(a)(b)'''

CDS 140a Winter 2011 Homework 4

2011-01-25T19:05:15Z

Genti:

{{HW draft}}
{{CDS homework
| instructor = G. Buzi, R. Murray
| course = ACM 101/AM 125a/CDS 140a
| semester = Winter 2011
| title = Problem Set #3
| issued = 15 Jan 2011 (Tue)
| due = 3 Feb 2011 (Thu)
}}

'''Note:''' In the upper left hand corner of the ''second'' page of your homework set, please put the number of hours that you spent on
this homework set (including reading).

'''Note:''' You can use Mathematica or similar software packages. However make sure you include all the steps in the solution write-up.

:1. '''Perko, Section 2.7, problem 1''' 
:2. '''Perko, Section 2.7, problem 2''' 
:3. '''Perko, Section 2.7, problem 3 ''' 
:4, 5. Choose any 2 of the following:
::* '''Perko, Section 2.7, problem 4'''
::* '''Perko, Section 2.7, problem 5'''
::* '''Perko, Section 2.7, problem 6'''
::* '''Perko, Section 2.8, problem 1'''
:6. '''Perko, Section 2.9, problem 2(a)(b)'''

ACM 101/AM 125b/CDS 140a, Winter 2011

2011-01-25T19:00:47Z

Genti:

{| width=100%
|-
| colspan=2 align=center |
Differential Equations and Dynamical Systems__NOTOC__
|- valign=top
| width=50% |
'''Instructors'''
* Richard Murray (CDS/BE)
* Gentian Buzi (CDS)
* Lectures: Tu/Th, 9-10:30, 105 ANB
| width=50% |
'''Teaching Assistants'''
* Molei Tao (CDS)
* Zhaoqian (Steven) Xie (CDS)
* Office hours: Wednesday 12-1, 107 ANB
|}

=== Course Description ===
Analytical methods for the formulation and solution of initial value problems for ordinary differential equations. Basics in topics in dynamical systems in Euclidean space, including equilibria, stability, phase diagrams, Lyapunov functions, periodic solutions, Poincaré-Bendixon theory, Poincaré maps. Introduction to simple bifurcations, including Hopf bifurcations, invariant and center manifolds.

===Announcements ===
* 18 Jan 2011: [[CDS 140a Winter 2011 Homework 3|HW #3]] is now posted; due 27 Jan 2011
* 11 Jan 2011: [[CDS 140a Winter 2011 Homework 2|HW #2]] is now posted; due 20 Jan 2011
* 6 Jan 2011: Office hours for HW #1 will be on 10 Jan (Mon) from 4-6 pm in 235 ANB; office hours for future weeks will be on Wednesdays from 12-2 in 235 ANB
* 6 Jan 2011: Course ombuds: Jeff Amelang and Matanya Horowitz
* 3 Jan 2011: [[CDS 140a Winter 2011 Homework 1|HW #1]] is now posted; due 11 Jan 2011
* 14 Nov 2010: web page creation

=== Lecture Schedule ===

{| width=100% border=1 cellspacing=0 cellpadding=5
|-
| '''Week'''
| '''Date'''
| '''Topic'''
| '''Reading'''
| '''Homework'''
|- valign=top
|- valign=top
| 1
| 4 Jan 6 Jan
| Linear Differential Equations I
* Course overview and administration
* Linear differential equations
* Matrix exponential, diagonalization
* Stable and unstable spaces
* Planar systems, behavior of solutions
|
Perko, 1.1-1.6 
Optional:
* J&S, Ch 1 
* J&S, 2.1-2.5
| [[CDS 140a Winter 2011 Homework 1|HW 1]]
|- valign=top
| 2
| 11 Jan 13 Jan
| Linear Differential Equations II
* S + N decomposition, Jordan form
* Stability theory
* Linear systems with inputs (nonhomogeneous systems)
* Boundary value problems
| Perko, 1.7-1.10 + notes
| [[CDS 140a Winter 2011 Homework 2|HW 2]]
|- valign=top
| 3
| 18 Jan 20 Jan
| Nonlinear differential equations
* Existence and uniqueness
* Flow of a differential equation
* Linearization
| Perko, 2.1-2.6
| [[CDS 140a Winter 2011 Homework 3|HW 3]]
|- valign=top
| 4
| 25 Jan 27 Jan
| Behavior of differential equations
* Stable and unstable manifolds ([[Media:cds140a-wi11-stablemanifoldNotes2.pdf|Some notes]])
* Stability and Lyapunov functions
* Planar systems, phase diagrams
| Perko, 2.7-2.10
| | [[CDS 140a Winter 2011 Homework 4|HW 4]]
|- valign=top
| 5
| 1 Feb* 3 Feb*
| Non-hyperbolic differential equations
* Center manifold theorem
* Normal forms
| Perko, 2.11-2.13
| 
|- valign=top
| 6
| 8 Feb* 10 Feb
| Hamiltonian systems
* Gradient and Hamiltonian systems
* Energy based stability methods
* Applications
| Perko 2.14 + notes
| 
|- valign=top
| 7
| 15 Feb 17 Feb
| Limit cycles
* Limit sets and attractors
* Periodic orbits and limit cycles
* Poincare' map
* Bendixson criterion for limit cycles in the plane
| Perko, 3.2-3.4, 3.9
| 
|- valign=top
| 8
| 22 Feb 24 Feb
| Bifurcations
* Structural stability
* Bifurcation of equilibrium points
* Hopf bifurcation
| Perko 4.1-4.4
| 
|- valign=top
| 9
| 1 Mar 3 Mar
| Advanced topics
* Higher co-dimension bifurcations
* Homoclinic bifurcation
| Perko, 4-3, 4.5-4.8, notes
| 
|- valign=top
| 10
| 8 Mar 
| Course review
| 
| 
|}

=== Textbook ===

The primary text for the course (available via the online bookstore) is
{|
|- valign=top
| align=right |  [Perko] 
| L. Perko, Differential Equations and Dynamical Systems, Third Edition. Springer, 2006.
|}

The following additional texts may be useful for some students (on reserve in SFL):
{|
|- valign=top
| align=right |  [J&S] 
| D. Jordan and P. Smith, Nonlinear Ordinary Differential Equations: An Introduction for Scientists and Engineers, Fourth Edition. Oxford University Press, 2007.
|}

=== Grading ===
The ﬁnal grade will be based on homework and a ﬁnal exam:
* Homework (75%) - There will be 9 one-week problem sets, due in class approximately one week after they are assigned. Late homework will not be accepted without prior permission from the instructor.
* Final exam (25%) - The ﬁnal will be handed out the last day of class and is due back at the end of ﬁnals week. Open book, time limit to be decided (likely N hours over a 4-8N hour period).

The lowest homework score you receive will be dropped in computing your homework average. In addition, if your score on the ﬁnal is higher than the weighted average of your homework and ﬁnal, your ﬁnal will be used to determine your course grade.

=== Collaboration Policy ===
Collaboration on homework assignments is encouraged. You may consult outside reference materials, other students, the TA, or the instructor. Use of solutions from previous years in the course or from other external sources is not allowed. All solutions that are handed should reﬂect your understanding of the subject matter at the time of writing.

No collaboration is allowed on the ﬁnal exam.

== Old Announcements ==

File:Cds140a-wi11-stablemanifoldNotes2.pdf

2011-01-25T18:59:29Z

Genti:

File:Cds140a-wi11-stablemanifoldNotes1.pdf

2011-01-25T18:54:16Z

Genti:

File:Cds140a-wi11-stablemanifoldNotes.pdf

2011-01-25T16:40:50Z

Genti:

CDS 140a Winter 2011 Homework 4

2011-01-25T08:20:57Z

{{HW draft}}
{{CDS homework
| instructor = G. Buzi, R. Murray
| course = ACM 101/AM 125a/CDS 140a
| semester = Winter 2011
| title = Problem Set #3
| issued = 15 Jan 2011 (Tue)
| due = 3 Feb 2011 (Thu)
}}

'''Note:''' In the upper left hand corner of the ''second'' page of your homework set, please put the number of hours that you spent on
this homework set (including reading).

<ol>
<li> '''Perko, Section 2.7, problem 1'''
</li>
<li> '''Perko, Section 2.7, problem 2'''
</li>
<li> '''Perko, Section 2.7, problem 3 '''
</li>
<li> '''Perko, Section 2.9, problem 2(a)(b)'''
</li>
<li> Choose any 2 of the following <ol>
* '''Perko, Section 2.7, problem 4'''
* '''Perko, Section 2.7, problem 5'''
* '''Perko, Section 2.7, problem 6'''
* '''Perko, Section 2.8, problem 1'''
</li>

ACM 101/AM 125b/CDS 140a, Winter 2011

2011-01-25T08:08:34Z

Genti:

{| width=100%
|-
| colspan=2 align=center |
Differential Equations and Dynamical Systems__NOTOC__
|- valign=top
| width=50% |
'''Instructors'''
* Richard Murray (CDS/BE)
* Gentian Buzi (CDS)
* Lectures: Tu/Th, 9-10:30, 105 ANB
| width=50% |
'''Teaching Assistants'''
* Molei Tao (CDS)
* Zhaoqian (Steven) Xie (CDS)
* Office hours: Wednesday 12-1, 107 ANB
|}

=== Course Description ===
Analytical methods for the formulation and solution of initial value problems for ordinary differential equations. Basics in topics in dynamical systems in Euclidean space, including equilibria, stability, phase diagrams, Lyapunov functions, periodic solutions, Poincaré-Bendixon theory, Poincaré maps. Introduction to simple bifurcations, including Hopf bifurcations, invariant and center manifolds.

===Announcements ===
* 18 Jan 2011: [[CDS 140a Winter 2011 Homework 3|HW #3]] is now posted; due 27 Jan 2011
* 11 Jan 2011: [[CDS 140a Winter 2011 Homework 2|HW #2]] is now posted; due 20 Jan 2011
* 6 Jan 2011: Office hours for HW #1 will be on 10 Jan (Mon) from 4-6 pm in 235 ANB; office hours for future weeks will be on Wednesdays from 12-2 in 235 ANB
* 6 Jan 2011: Course ombuds: Jeff Amelang and Matanya Horowitz
* 3 Jan 2011: [[CDS 140a Winter 2011 Homework 1|HW #1]] is now posted; due 11 Jan 2011
* 14 Nov 2010: web page creation

=== Lecture Schedule ===

{| width=100% border=1 cellspacing=0 cellpadding=5
|-
| '''Week'''
| '''Date'''
| '''Topic'''
| '''Reading'''
| '''Homework'''
|- valign=top
|- valign=top
| 1
| 4 Jan 6 Jan
| Linear Differential Equations I
* Course overview and administration
* Linear differential equations
* Matrix exponential, diagonalization
* Stable and unstable spaces
* Planar systems, behavior of solutions
|
Perko, 1.1-1.6 
Optional:
* J&S, Ch 1 
* J&S, 2.1-2.5
| [[CDS 140a Winter 2011 Homework 1|HW 1]]
|- valign=top
| 2
| 11 Jan 13 Jan
| Linear Differential Equations II
* S + N decomposition, Jordan form
* Stability theory
* Linear systems with inputs (nonhomogeneous systems)
* Boundary value problems
| Perko, 1.7-1.10 + notes
| [[CDS 140a Winter 2011 Homework 2|HW 2]]
|- valign=top
| 3
| 18 Jan 20 Jan
| Nonlinear differential equations
* Existence and uniqueness
* Flow of a differential equation
* Linearization
| Perko, 2.1-2.6
| [[CDS 140a Winter 2011 Homework 3|HW 3]]
|- valign=top
| 4
| 25 Jan 27 Jan
| Behavior of differential equations
* Stable and unstable manifolds
* Stability and Lyapunov functions
* Planar systems, phase diagrams
| Perko, 2.7-2.10
| | [[CDS 140a Winter 2011 Homework 4|HW 4]]
|- valign=top
| 5
| 1 Feb* 3 Feb*
| Non-hyperbolic differential equations
* Center manifold theorem
* Normal forms
| Perko, 2.11-2.13
| 
|- valign=top
| 6
| 8 Feb* 10 Feb
| Hamiltonian systems
* Gradient and Hamiltonian systems
* Energy based stability methods
* Applications
| Perko 2.14 + notes
| 
|- valign=top
| 7
| 15 Feb 17 Feb
| Limit cycles
* Limit sets and attractors
* Periodic orbits and limit cycles
* Poincare' map
* Bendixson criterion for limit cycles in the plane
| Perko, 3.2-3.4, 3.9
| 
|- valign=top
| 8
| 22 Feb 24 Feb
| Bifurcations
* Structural stability
* Bifurcation of equilibrium points
* Hopf bifurcation
| Perko 4.1-4.4
| 
|- valign=top
| 9
| 1 Mar 3 Mar
| Advanced topics
* Higher co-dimension bifurcations
* Homoclinic bifurcation
| Perko, 4-3, 4.5-4.8, notes
| 
|- valign=top
| 10
| 8 Mar 
| Course review
| 
| 
|}

=== Textbook ===

The primary text for the course (available via the online bookstore) is
{|
|- valign=top
| align=right |  [Perko] 
| L. Perko, Differential Equations and Dynamical Systems, Third Edition. Springer, 2006.
|}

The following additional texts may be useful for some students (on reserve in SFL):
{|
|- valign=top
| align=right |  [J&S] 
| D. Jordan and P. Smith, Nonlinear Ordinary Differential Equations: An Introduction for Scientists and Engineers, Fourth Edition. Oxford University Press, 2007.
|}

=== Grading ===
The ﬁnal grade will be based on homework and a ﬁnal exam:
* Homework (75%) - There will be 9 one-week problem sets, due in class approximately one week after they are assigned. Late homework will not be accepted without prior permission from the instructor.
* Final exam (25%) - The ﬁnal will be handed out the last day of class and is due back at the end of ﬁnals week. Open book, time limit to be decided (likely N hours over a 4-8N hour period).

The lowest homework score you receive will be dropped in computing your homework average. In addition, if your score on the ﬁnal is higher than the weighted average of your homework and ﬁnal, your ﬁnal will be used to determine your course grade.

=== Collaboration Policy ===
Collaboration on homework assignments is encouraged. You may consult outside reference materials, other students, the TA, or the instructor. Use of solutions from previous years in the course or from other external sources is not allowed. All solutions that are handed should reﬂect your understanding of the subject matter at the time of writing.

No collaboration is allowed on the ﬁnal exam.

== Old Announcements ==

CDS 140a Winter 2011 Homework 3

2011-01-19T03:14:16Z

Genti:

{{CDS homework
| instructor = G. Buzi, R. Murray
| course = ACM 101/AM 125a/CDS 140a
| semester = Winter 2011
| title = Problem Set #3
| issued = 18 Jan 2011 (Tue)
| due = 27 Jan 2011 (Thu)
}}

'''Note:''' In the upper left hand corner of the ''second'' page of your homework set, please put the number of hours that you spent on
this homework set (including reading).

<ol>
<li> '''Perko, Section 2.1, problem 4'''
</li>
<li> '''Perko, Section 2.2, problem 3'''
</li>
<li> '''Perko, Section 2.3, problem 2 (a)'''
</li>
<li> '''Perko, Section 2.4, problem 2 (a) (b)'''
</li>
<li> '''Perko, Section 2.5, problem 5'''
</li>

<li> '''Perko, Section 2.6, problem 3'''
</li>

* The problems can be found [[Media:cds140a-wi11-hw3.pdf| here]] in case you don't have access to Perko. However, in the case of discrepancy, you should use Perko as the definitive source of the problem statement.

CDS 140a Winter 2011 Homework 3

2011-01-19T03:12:18Z

Genti:

{{HW draft}}
{{CDS homework
| instructor = G. Buzi, R. Murray
| course = ACM 101/AM 125a/CDS 140a
| semester = Winter 2011
| title = Problem Set #3
| issued = 18 Jan 2011 (Tue)
| due = 27 Jan 2011 (Thu)
}}

'''Note:''' In the upper left hand corner of the ''second'' page of your homework set, please put the number of hours that you spent on
this homework set (including reading).

<ol>
<li> '''Perko, Section 2.1, problem 4'''
</li>
<li> '''Perko, Section 2.2, problem 3'''
</li>
<li> '''Perko, Section 2.3, problem 2 (a)'''
</li>
<li> '''Perko, Section 2.4, problem 2 (a) (b)'''
</li>
<li> '''Perko, Section 2.5, problem 5'''
</li>

<li> '''Perko, Section 2.6, problem 3'''
</li>

* The problems can be found [[Media:cds140a-wi11-hw3.pdf| here]] in case you don't have access to Perko. However, in the case of discrepancy, you should use Perko as the definitive source of the problem statement.

ACM 101/AM 125b/CDS 140a, Winter 2011

2011-01-19T01:43:45Z

Genti:

{| width=100%
|-
| colspan=2 align=center |
Differential Equations and Dynamical Systems__NOTOC__
|- valign=top
| width=50% |
'''Instructors'''
* Richard Murray (CDS/BE)
* Gentian Buzi (CDS)
* Lectures: Tu/Th, 9-10:30, 105 ANB
| width=50% |
'''Teaching Assistants'''
* Molei Tao (CDS)
* Zhaoqian (Steven) Xie (CDS)
* Office hours: Wednesday 12-1, 107 ANB
|}

=== Course Description ===
Analytical methods for the formulation and solution of initial value problems for ordinary differential equations. Basics in topics in dynamical systems in Euclidean space, including equilibria, stability, phase diagrams, Lyapunov functions, periodic solutions, Poincaré-Bendixon theory, Poincaré maps. Introduction to simple bifurcations, including Hopf bifurcations, invariant and center manifolds.

===Announcements ===
* 18 Jan 2011: [[CDS 140a Winter 2011 Homework 3|HW #3]] is now posted; due 27 Jan 2011
* 11 Jan 2011: [[CDS 140a Winter 2011 Homework 2|HW #2]] is now posted; due 20 Jan 2011
* 6 Jan 2011: Office hours for HW #1 will be on 10 Jan (Mon) from 4-6 pm in 235 ANB; office hours for future weeks will be on Wednesdays from 12-2 in 235 ANB
* 6 Jan 2011: Course ombuds: Jeff Amelang and Matanya Horowitz
* 3 Jan 2011: [[CDS 140a Winter 2011 Homework 1|HW #1]] is now posted; due 11 Jan 2011
* 14 Nov 2010: web page creation

=== Lecture Schedule ===

{| width=100% border=1 cellspacing=0 cellpadding=5
|-
| '''Week'''
| '''Date'''
| '''Topic'''
| '''Reading'''
| '''Homework'''
|- valign=top
|- valign=top
| 1
| 4 Jan 6 Jan
| Linear Differential Equations I
* Course overview and administration
* Linear differential equations
* Matrix exponential, diagonalization
* Stable and unstable spaces
* Planar systems, behavior of solutions
|
Perko, 1.1-1.6 
Optional:
* J&S, Ch 1 
* J&S, 2.1-2.5
| [[CDS 140a Winter 2011 Homework 1|HW 1]]
|- valign=top
| 2
| 11 Jan 13 Jan
| Linear Differential Equations II
* S + N decomposition, Jordan form
* Stability theory
* Linear systems with inputs (nonhomogeneous systems)
* Boundary value problems
| Perko, 1.7-1.10 + notes
| [[CDS 140a Winter 2011 Homework 2|HW 2]]
|- valign=top
| 3
| 18 Jan 20 Jan
| Nonlinear differential equations
* Existence and uniqueness
* Flow of a differential equation
* Linearization
| Perko, 2.1-2.6
| [[CDS 140a Winter 2011 Homework 3|HW 3]]
|- valign=top
| 4
| 25 Jan 27 Jan
| Behavior of differential equations
* Stable and unstable manifolds
* Stability and Lyapunov functions
* Planar systems, phase diagrams
| Perko, 2.6-2.10
| 
|- valign=top
| 5
| 1 Feb* 3 Feb*
| Non-hyperbolic differential equations
* Center manifold theorem
* Normal forms
| Perko, 2.11-2.13
| 
|- valign=top
| 6
| 8 Feb* 10 Feb
| Hamiltonian systems
* Gradient and Hamiltonian systems
* Energy based stability methods
* Applications
| Perko 2.14 + notes
| 
|- valign=top
| 7
| 15 Feb 17 Feb
| Limit cycles
* Limit sets and attractors
* Periodic orbits and limit cycles
* Poincare' map
* Bendixson criterion for limit cycles in the plane
| Perko, 3.2-3.4, 3.9
| 
|- valign=top
| 8
| 22 Feb 24 Feb
| Bifurcations
* Structural stability
* Bifurcation of equilibrium points
* Hopf bifurcation
| Perko 4.1-4.4
| 
|- valign=top
| 9
| 1 Mar 3 Mar
| Advanced topics
* Higher co-dimension bifurcations
* Homoclinic bifurcation
| Perko, 4-3, 4.5-4.8, notes
| 
|- valign=top
| 10
| 8 Mar 
| Course review
| 
| 
|}

=== Textbook ===

The primary text for the course (available via the online bookstore) is
{|
|- valign=top
| align=right |  [Perko] 
| L. Perko, Differential Equations and Dynamical Systems, Third Edition. Springer, 2006.
|}

The following additional texts may be useful for some students (on reserve in SFL):
{|
|- valign=top
| align=right |  [J&S] 
| D. Jordan and P. Smith, Nonlinear Ordinary Differential Equations: An Introduction for Scientists and Engineers, Fourth Edition. Oxford University Press, 2007.
|}

=== Grading ===
The ﬁnal grade will be based on homework and a ﬁnal exam:
* Homework (75%) - There will be 9 one-week problem sets, due in class approximately one week after they are assigned. Late homework will not be accepted without prior permission from the instructor.
* Final exam (25%) - The ﬁnal will be handed out the last day of class and is due back at the end of ﬁnals week. Open book, time limit to be decided (likely N hours over a 4-8N hour period).

The lowest homework score you receive will be dropped in computing your homework average. In addition, if your score on the ﬁnal is higher than the weighted average of your homework and ﬁnal, your ﬁnal will be used to determine your course grade.

=== Collaboration Policy ===
Collaboration on homework assignments is encouraged. You may consult outside reference materials, other students, the TA, or the instructor. Use of solutions from previous years in the course or from other external sources is not allowed. All solutions that are handed should reﬂect your understanding of the subject matter at the time of writing.

No collaboration is allowed on the ﬁnal exam.

== Old Announcements ==

CDS 140a Winter 2011 Homework 3

2011-01-19T01:39:49Z

Genti:

{{HW draft}}
{{CDS homework
| instructor = G. Buzi, R. Murray
| course = ACM 101/AM 125a/CDS 140a
| semester = Winter 2011
| title = Problem Set #3
| issued = 18 Jan 2011 (Tue)
| due = 27 Jan 2011 (Thu)
}}

'''Note:''' In the upper left hand corner of the ''second'' page of your homework set, please put the number of hours that you spent on
this homework set (including reading).

<ol>
<li> '''Perko, Section 2.1, problem 4'''
</li>
<li> '''Perko, Section 2.2, problem 3'''
</li>
<li> '''Perko, Section 2.3, problem 2 (a)'''
</li>
<li> '''Perko, Section 2.4, problem 2 (a) (b)'''
</li>
<li> '''Perko, Section 2.5, problem 5'''
</li>

<li> '''Perko, Section 2.6, problem 3'''
</li>

* The problems can be found here [[Media:cds140a-wi11-hw3.pdf]] in case you don't have access to Perko. However, in the case of discrepancy, you should use Perko as the definitive source of the problem statement.

File:Cds140a-wi11-hw3.pdf

2011-01-19T01:33:05Z

Genti:

File:Hw3.pdf

2011-01-19T01:15:51Z

Genti: uploaded a new version of "File:Hw3.pdf"

ACM 101/AM 125b/CDS 140a, Winter 2011

2011-01-17T19:11:58Z

Genti: /* Lecture Schedule */

{| width=100%
|-
| colspan=2 align=center |
Differential Equations and Dynamical Systems__NOTOC__
|- valign=top
| width=50% |
'''Instructors'''
* Richard Murray (CDS/BE)
* Gentian Buzi (CDS)
* Lectures: Tu/Th, 9-10:30, 105 ANB
| width=50% |
'''Teaching Assistants'''
* Molei Tao (CDS)
* Zhaoqian (Steven) Xie (CDS)
* Office hours: Wednesday 12-1, 107 ANB
|}

=== Course Description ===
Analytical methods for the formulation and solution of initial value problems for ordinary differential equations. Basics in topics in dynamical systems in Euclidean space, including equilibria, stability, phase diagrams, Lyapunov functions, periodic solutions, Poincaré-Bendixon theory, Poincaré maps. Introduction to simple bifurcations, including Hopf bifurcations, invariant and center manifolds.

===Announcements ===
* 11 Jan 2011: [[CDS 140a Winter 2011 Homework 2|HW #2]] is now posted; due 20 Jan 2011
* 6 Jan 2011: Office hours for HW #1 will be on 10 Jan (Mon) from 4-6 pm in 235 ANB; office hours for future weeks will be on Wednesdays from 12-2 in 235 ANB
* 6 Jan 2011: Course ombuds: Jeff Amelang and Matanya Horowitz
* 3 Jan 2011: [[CDS 140a Winter 2011 Homework 1|HW #1]] is now posted; due 11 Jan 2011
* 14 Nov 2010: web page creation

=== Lecture Schedule ===

{| width=100% border=1 cellspacing=0 cellpadding=5
|-
| '''Week'''
| '''Date'''
| '''Topic'''
| '''Reading'''
| '''Homework'''
|- valign=top
|- valign=top
| 1
| 4 Jan 6 Jan
| Linear Differential Equations I
* Course overview and administration
* Linear differential equations
* Matrix exponential, diagonalization
* Stable and unstable spaces
* Planar systems, behavior of solutions
|
Perko, 1.1-1.6 
Optional:
* J&S, Ch 1 
* J&S, 2.1-2.5
| [[CDS 140a Winter 2011 Homework 1|HW 1]]
|- valign=top
| 2
| 11 Jan 13 Jan
| Linear Differential Equations II
* S + N decomposition, Jordan form
* Stability theory
* Linear systems with inputs (nonhomogeneous systems)
* Boundary value problems
| Perko, 1.7-1.10 + notes
| [[CDS 140a Winter 2011 Homework 2|HW 2]]
|- valign=top
| 3
| 18 Jan 20 Jan
| Nonlinear differential equations
* Existence and uniqueness
* Flow of a differential equation
* Linearization
| Perko, 2.1-2.6
| [[CDS 140a Winter 2011 Homework 3|HW 3]]
|- valign=top
| 4
| 25 Jan 27 Jan
| Behavior of differential equations
* Stable and unstable manifolds
* Stability and Lyapunov functions
* Planar systems, phase diagrams
| Perko, 2.6-2.10
| 
|- valign=top
| 5
| 1 Feb* 3 Feb*
| Non-hyperbolic differential equations
* Center manifold theorem
* Normal forms
| Perko, 2.11-2.13
| 
|- valign=top
| 6
| 8 Feb* 10 Feb
| Hamiltonian systems
* Gradient and Hamiltonian systems
* Energy based stability methods
* Applications
| Perko 2.14 + notes
| 
|- valign=top
| 7
| 15 Feb 17 Feb
| Limit cycles
* Limit sets and attractors
* Periodic orbits and limit cycles
* Poincare' map
* Bendixson criterion for limit cycles in the plane
| Perko, 3.2-3.4, 3.9
| 
|- valign=top
| 8
| 22 Feb 24 Feb
| Bifurcations
* Structural stability
* Bifurcation of equilibrium points
* Hopf bifurcation
| Perko 4.1-4.4
| 
|- valign=top
| 9
| 1 Mar 3 Mar
| Advanced topics
* Higher co-dimension bifurcations
* Homoclinic bifurcation
| Perko, 4-3, 4.5-4.8, notes
| 
|- valign=top
| 10
| 8 Mar 
| Course review
| 
| 
|}

=== Textbook ===

The primary text for the course (available via the online bookstore) is
{|
|- valign=top
| align=right |  [Perko] 
| L. Perko, Differential Equations and Dynamical Systems, Third Edition. Springer, 2006.
|}

The following additional texts may be useful for some students (on reserve in SFL):
{|
|- valign=top
| align=right |  [J&S] 
| D. Jordan and P. Smith, Nonlinear Ordinary Differential Equations: An Introduction for Scientists and Engineers, Fourth Edition. Oxford University Press, 2007.
|}

=== Grading ===
The ﬁnal grade will be based on homework and a ﬁnal exam:
* Homework (75%) - There will be 9 one-week problem sets, due in class approximately one week after they are assigned. Late homework will not be accepted without prior permission from the instructor.
* Final exam (25%) - The ﬁnal will be handed out the last day of class and is due back at the end of ﬁnals week. Open book, time limit to be decided (likely N hours over a 4-8N hour period).

The lowest homework score you receive will be dropped in computing your homework average. In addition, if your score on the ﬁnal is higher than the weighted average of your homework and ﬁnal, your ﬁnal will be used to determine your course grade.

=== Collaboration Policy ===
Collaboration on homework assignments is encouraged. You may consult outside reference materials, other students, the TA, or the instructor. Use of solutions from previous years in the course or from other external sources is not allowed. All solutions that are handed should reﬂect your understanding of the subject matter at the time of writing.

No collaboration is allowed on the ﬁnal exam.

== Old Announcements ==

CDS 140a Winter 2011 Homework 3

2011-01-17T19:11:12Z

Genti: Created page with '{{CDS homework | instructor = R. Murray, G. Buzi | course = ACM 101/AM 125a/CDS 140a | semester = Winter 2011 | title = Problem Set #3 | issued = 18 Jan 2011 (Tue) | due = …'

{{CDS homework
| instructor = R. Murray, G. Buzi
| course = ACM 101/AM 125a/CDS 140a
| semester = Winter 2011
| title = Problem Set #3
| issued = 18 Jan 2011 (Tue)
| due = 27 Jan 2011 (Thu)
}}

'''Note:''' In the upper left hand corner of the ''second'' page of your homework set, please put the number of hours that you spent on
this homework set (including reading).

<ol>
<li> '''Perko, Section 2.1, problem 4'''
</li>
<li> '''Perko, Section 2.2, problem 3'''
</li>
<li> '''Perko, Section 2.3, problem 2 (a)'''
</li>
<li> '''Perko, Section 2.4, problem 2 (a) (b)'''
</li>
<li> '''Perko, Section 2.5, problem 5'''
</li>

<li> '''Perko, Section 2.6, problem 3'''
</li>

ACM 101/AM 125b/CDS 140a, Winter 2011

2011-01-11T17:01:23Z

Genti:

{| width=100%
|-
| colspan=2 align=center |
Differential Equations and Dynamical Systems__NOTOC__
|- valign=top
| width=50% |
'''Instructors'''
* Richard Murray (CDS/BE)
* Gentian Buzi (CDS)
* Lectures: Tu/Th, 9-10:30, 105 ANB
| width=50% |
'''Teaching Assistants'''
* Molei Tao (CDS)
* Zhaoqian (Steven) Xie (CDS)
* Office hours: Wednesday 12-2, 107 ANB
|}

=== Course Description ===
Analytical methods for the formulation and solution of initial value problems for ordinary differential equations. Basics in topics in dynamical systems in Euclidean space, including equilibria, stability, phase diagrams, Lyapunov functions, periodic solutions, Poincaré-Bendixon theory, Poincaré maps. Introduction to simple bifurcations, including Hopf bifurcations, invariant and center manifolds.

===Announcements ===
* 6 Jan 2011: Office hours for HW #1 will be on 10 Jan (Mon) from 4-6 pm in 235 ANB; office hours for future weeks will be on Wednesdays from 12-2 in 235 ANB
* 6 Jan 2011: Course ombuds: Jeff Amelang and Matanya Horowitz
* 3 Jan 2011: [[CDS 140a Winter 2011 Homework 1|HW #1]] is now posted; due 11 Jan 2011
* 14 Nov 2010: web page creation

=== Lecture Schedule ===

{| width=100% border=1 cellspacing=0 cellpadding=5
|-
| '''Week'''
| '''Date'''
| '''Topic'''
| '''Reading'''
| '''Homework'''
|- valign=top
|- valign=top
| 1
| 4 Jan 6 Jan
| Linear Differential Equations I
* Course overview and administration
* Linear differential equations
* Matrix exponential, diagonalization
* Stable and unstable spaces
* Planar systems, behavior of solutions
|
Perko, 1.1-1.6 
Optional:
* J&S, Ch 1 
* J&S, 2.1-2.5
| [[CDS 140a Winter 2011 Homework 1|HW 1]]
|- valign=top
| 2
| 11 Jan 13 Jan
| Linear Differential Equations II
* S + N decomposition, Jordan form
* Stability theory
* Linear systems with inputs (nonhomogeneous systems)
* Boundary value problems
| Perko, 1.7-1.10 + notes
| [[CDS 140a Winter 2011 Homework 2|HW 2]]
|- valign=top
| 3
| 18 Jan 20 Jan
| Nonlinear differential equations
* Existence and uniqueness
* Flow of a differential equation
* Linearization
| Perko, 2.1-2.6
| 
|- valign=top
| 4
| 25 Jan 27 Jan
| Behavior of differential equations
* Stable and unstable manifolds
* Stability and Lyapunov functions
* Planar systems, phase diagrams
| Perko, 2.6-2.10
| 
|- valign=top
| 5
| 1 Feb* 3 Feb*
| Non-hyperbolic differential equations
* Center manifold theorem
* Normal forms
| Perko, 2.11-2.13
| 
|- valign=top
| 6
| 8 Feb* 10 Feb
| Hamiltonian systems
* Gradient and Hamiltonian systems
* Energy based stability methods
* Applications
| Perko 2.14 + notes
| 
|- valign=top
| 7
| 15 Feb 17 Feb
| Limit cycles
* Limit sets and attractors
* Periodic orbits and limit cycles
* Poincare' map
* Bendixson criterion for limit cycles in the plane
| Perko, 3.2-3.4, 3.9
| 
|- valign=top
| 8
| 22 Feb 24 Feb
| Bifurcations
* Structural stability
* Bifurcation of equilibrium points
* Hopf bifurcation
| Perko 4.1-4.4
| 
|- valign=top
| 9
| 1 Mar 3 Mar
| Advanced topics
* Higher co-dimension bifurcations
* Homoclinic bifurcation
| Perko, 4-3, 4.5-4.8, notes
| 
|- valign=top
| 10
| 8 Mar 
| Course review
| 
| 
|}

=== Textbook ===

The primary text for the course (available via the online bookstore) is
{|
|- valign=top
| align=right |  [Perko] 
| L. Perko, Differential Equations and Dynamical Systems, Third Edition. Springer, 2006.
|}

The following additional texts may be useful for some students (on reserve in SFL):
{|
|- valign=top
| align=right |  [J&S] 
| D. Jordan and P. Smith, Nonlinear Ordinary Differential Equations: An Introduction for Scientists and Engineers, Fourth Edition. Oxford University Press, 2007.
|}

=== Grading ===
The ﬁnal grade will be based on homework and a ﬁnal exam:
* Homework (75%) - There will be 9 one-week problem sets, due in class approximately one week after they are assigned. Late homework will not be accepted without prior permission from the instructor.
* Final exam (25%) - The ﬁnal will be handed out the last day of class and is due back at the end of ﬁnals week. Open book, time limit to be decided (likely N hours over a 4-8N hour period).

The lowest homework score you receive will be dropped in computing your homework average. In addition, if your score on the ﬁnal is higher than the weighted average of your homework and ﬁnal, your ﬁnal will be used to determine your course grade.

=== Collaboration Policy ===
Collaboration on homework assignments is encouraged. You may consult outside reference materials, other students, the TA, or the instructor. Use of solutions from previous years in the course or from other external sources is not allowed. All solutions that are handed should reﬂect your understanding of the subject matter at the time of writing.

No collaboration is allowed on the ﬁnal exam.

== Old Announcements ==

Pablo Parrilo, Nov 2010

2010-11-19T19:58:27Z

Genti: /* Agenda */

Pablo Parrilo will be visiting Caltech on 23 Nov 2010 (Tue). Sign up for a time to meet with him below.

=== Agenda ===
{{agenda begin}}
{{agenda item|9:30a|Open}}
{{agenda item|10:15a|Richard Murray (109 Steele)}}
{{agenda item|11:00a|Seminar: 214 Steele}}
{{agenda item|12:00p|Lunch with John, (faculty: add your name to the list if you want to come)}}
{{agenda item|1:30p|Open}}
{{agenda item|2:15|John Doyle (Annenberg)}}
{{agenda item|2:30p|CDS 212 (Annenberg)}}
{{agenda item|4:00p|Genti (Annenberg)}}
{{agenda item|4:45p|Open}}
{{agenda end}}

=== Seminar ===

'''FLOWS AND DECOMPOSITIONS OF GAMES: HARMONIC AND POTENTIAL GAMES'''

Pablo A. Parrilo (Massachusetts Institute of Technology)

Tuesday, November 23, 2010 
11:00 AM to 12:00 PM 
Steele 214

Exact potential games are those where the preferences of the strategy
profiles of the different players are globally consistent, and therefore
the players' payoffs can be aggregated through a joint function. In this
talk, we analyze the general situation where there are local or global
inconsistencies between the preferences of the different players. For
this, we introduce a natural decomposition of multiplayer games in terms
of potential and harmonic components. Besides its intrinsic interest,
this decomposition facilitates the study of equilibrium and convergence
properties of natural game dynamics. We discuss the implications for
cooperative control problems, pricing schemes, and efficiency loss, and
illustrate the results and techniques through an example of power
control in wireless networks. Joint work with Ozan Candogan, Ishai
Menache, and Asu Ozdaglar (MIT), http://arxiv.org/abs/1005.2405