CDS 140, Winter 2015: Difference between revisions
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'''Teaching Assistants''' | '''Teaching Assistants''' | ||
* | * Vanessa Jonsson (CDS) | ||
* Contact: cds140-tas@cds.caltech.edu | * Contact: cds140-tas@cds.caltech.edu | ||
* Office hours: TBD | * Office hours: TBD | ||
| Line 31: | Line 31: | ||
|- valign=top | |- valign=top | ||
|- valign=top | |- valign=top | ||
| | | 5 Jan <br> 7 Jan | ||
| Linear Differential Equations | | Linear Differential Equations | ||
* Course overview and administration | * Course overview and administration | ||
* Linear differential equations | * Linear differential equations | ||
* Matrix exponential, diagonalization | * Matrix exponential, diagonalization | ||
* Stable and unstable spaces | * Stable and unstable spaces | ||
* | * S + N decomposition, Jordan form | ||
| | | | ||
Perko, 1.1-1. | Perko, 1.1-1.10<br> | ||
| [[CDS 140a Winter | | [[CDS 140a Winter 2015 Homework 1|HW 1]] <br> Due: 14 Jan (Wed) | ||
|- valign=top | |- valign=top | ||
| | | 12 Jan <br> 14 Jan <br> 16 Jan | ||
| Nonlinear differential equations | | Nonlinear differential equations | ||
* Existence and uniqueness | * Existence and uniqueness | ||
| Line 56: | Line 48: | ||
* Linearization | * Linearization | ||
| Perko, 2.1-2.6 | | Perko, 2.1-2.6 | ||
| [[CDS 140a Winter | | [[CDS 140a Winter 2015 Homework 2|HW 2]] <br> Due: 21 Jan (Wed) | ||
|- valign=top | |- valign=top | ||
| | | 21 Jan <br> 23 Jan | ||
| Behavior of differential equations | | Behavior of differential equations | ||
* Stable and unstable manifolds | * Stable and unstable manifolds | ||
* Stability of equilibrium points for planar systems | * Stability of equilibrium points for planar systems | ||
| Perko, 2.7-2.10 | | Perko, 2.7-2.10 | ||
| [[CDS 140a Winter 2015 Homework 3|HW 3]] <br> Due: 28 Jan (Wed) | |||
|- valign=top | |- valign=top | ||
| | | 26 Jan <br> 28 Jan <br> 30 Jan | ||
| Non-hyperbolic differential equations | | Non-hyperbolic differential equations | ||
* Lyapunov functions | * Lyapunov functions | ||
* Center manifold theorem | * Center manifold theorem | ||
| Perko, 2.11-2.13 | | Perko, 2.11-2.13 | ||
| [[CDS 140a Winter | | [[CDS 140a Winter 2015 Homework 4|HW 4]] <br> Due: 4 Feb (Wed) | ||
|- valign=top | |- valign=top | ||
| | | 4 Feb <br> 6 Feb | ||
| Global behavior | | Global behavior | ||
* Limit sets and attractors | * Limit sets and attractors | ||
| Line 78: | Line 70: | ||
* Periodic orbits and limit cycles | * Periodic orbits and limit cycles | ||
| Perko, 3.1-3.3 | | Perko, 3.1-3.3 | ||
| [[CDS 140a Winter | | [[CDS 140a Winter 2015 Homework 5|HW 5]] <br> Due: 11 Feb (Wed) | ||
|- valign=top | |- valign=top | ||
| | | 9 Feb <br> 11 Feb | ||
| Limit cycles | | Limit cycles | ||
* Poincare' map | * Poincare' map | ||
* Bendixson criterion for limit cycles in the plane | * Bendixson criterion for limit cycles in the plane | ||
| Perko, 3.4-3.5, 3.7 | | Perko, 3.4-3.5, 3.7 | ||
| [[CDS 140a Winter | | [[CDS 140a Winter 2015 Homework 6|HW 6]] <br> Due: 18 Feb (Wed) | ||
|- valign=top | |- valign=top | ||
| | | 18 Feb <br> 20 Feb | ||
| Bifurcations | | Bifurcations | ||
* Sensitivity analysis | * Sensitivity analysis | ||
| Line 94: | Line 86: | ||
| Perko 4.1-4.2 + notes | | Perko 4.1-4.2 + notes | ||
* [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/L8-1_bfs_sensitivity.pdf BFS notes on parameter sensitivity] | ||
| [[CDS 140a Winter | | [[CDS 140a Winter 2015 Homework 7|HW 7]] <br> Due: 25 Feb (Wed) | ||
|- valign=top | |- valign=top | ||
| | | 23 Feb <br> 25 Feb <br> 27 Feb | ||
| Bifurcations | | Bifurcations | ||
* Hopf bifurcation | * Hopf bifurcation | ||
* Application example: rotating stall and surge in turbomachinery | * Application example: rotating stall and surge in turbomachinery | ||
| Perko 4.3-4.5 + notes | | Perko 4.3-4.5 + notes | ||
| [[CDS 140a Winter | | [[CDS 140a Winter 2015 Homework 8|HW 8]] <br> Due: 4 Mar (Wed) | ||
|- valign=top | |||
| 2 Mar <br> 6 Mar <br> 9 Mar | |||
| Special topics | |||
| TBD | |||
| [[CDS 140a Winter 2015 Homework 9|HW 9]] <br> Due: 13 Mar (Fri) | |||
|- valign=top | |- valign=top | ||
| 11 Mar* <br> | | 11 Mar* <br> | ||
| Course review | | Course review | ||
| <!-- Reading --> | | <!-- Reading --> | ||
| Final exam <br> Due: | | Final exam <br> Due: 18 Mar (Wed). Pick up from Nikki Fountleroy, 107 Steele Lab | ||
|} | |} | ||
Revision as of 15:07, 26 December 2014
|
Differential Equations and Dynamical Systems | |
|
Instructors
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Teaching Assistants
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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.
Lecture Schedule
| Date | Topic | Reading | Homework |
| 5 Jan 7 Jan |
Linear Differential Equations
|
Perko, 1.1-1.10 |
HW 1 Due: 14 Jan (Wed) |
| 12 Jan 14 Jan 16 Jan |
Nonlinear differential equations
|
Perko, 2.1-2.6 | HW 2 Due: 21 Jan (Wed) |
| 21 Jan 23 Jan |
Behavior of differential equations
|
Perko, 2.7-2.10 | HW 3 Due: 28 Jan (Wed) |
| 26 Jan 28 Jan 30 Jan |
Non-hyperbolic differential equations
|
Perko, 2.11-2.13 | HW 4 Due: 4 Feb (Wed) |
| 4 Feb 6 Feb |
Global behavior
|
Perko, 3.1-3.3 | HW 5 Due: 11 Feb (Wed) |
| 9 Feb 11 Feb |
Limit cycles
|
Perko, 3.4-3.5, 3.7 | HW 6 Due: 18 Feb (Wed) |
| 18 Feb 20 Feb |
Bifurcations
|
Perko 4.1-4.2 + notes | HW 7 Due: 25 Feb (Wed) |
| 23 Feb 25 Feb 27 Feb |
Bifurcations
|
Perko 4.3-4.5 + notes | HW 8 Due: 4 Mar (Wed) |
| 2 Mar 6 Mar 9 Mar |
Special topics | TBD | HW 9 Due: 13 Mar (Fri) |
| 11 Mar* |
Course review | Final exam Due: 18 Mar (Wed). Pick up from Nikki Fountleroy, 107 Steele Lab |
Textbook
The primary text for the course (available via the online bookstore) is
| [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):
| [J&S] | D. Jordan and P. Smith, Nonlinear Ordinary Differential Equations: An Introduction for Scientists and Engineers, Fourth Edition. Oxford University Press, 2007. |
| [Ver] | F. Verhulst, Nonlinear Differential Equations and Dynamical Systems, Second Edition. Springer, 2006. |
Grading
The final grade will be based on homework and a final exam:
- Homework (75%) - There will be 8 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.
You can use MATLAB, Mathematica or a similar programs, but you must show the steps that would be required to obtain your answers by hand (to make sure you understand the techniques).
No collaboration is allowed on the final exam. You will also not be allowed to use computers, but the problems should be such that extensive computation is not required.
