ACM 101b/AM 125b/CDS 140a, Winter 2014 - Revision history

Murray: /* Lecture Schedule */

2014-03-30T16:25:58Z

Lecture Schedule

← Older revision		Revision as of 16:25, 30 March 2014
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	\| Bifurcations		\| Bifurcations
	* Hopf bifurcation		* Hopf bifurcation
			* Application example: rotating stall and surge in turbomachinery
	\| Perko 4.3-4.5 + notes		\| Perko 4.3-4.5 + notes
	\| [[CDS 140a Winter 2014 Homework 9\|HW 9]] <br> Due: 12 Mar (Wed)		\| [[CDS 140a Winter 2014 Homework 9\|HW 9]] <br> Due: 12 Mar (Wed)

Murray: /* Lecture Schedule */

2014-03-30T16:25:09Z

Lecture Schedule

← Older revision		Revision as of 16:25, 30 March 2014
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	* Stability of equilibrium points for planar systems		* Stability of equilibrium points for planar systems
	\| Perko, 2.7-2.10		\| Perko, 2.7-2.10
	~~<!--~~
	* [[Media:cds140a-wi11-Week4Notes.pdf\|Some notes]]
	* [[Media:cds140a-wi11-InvManRemark.pdf\|Remark on invariant manifolds]]
	~~-->~~
	\| \| [[CDS 140a Winter 2014 Homework 4\|HW 4]] <br> Due: 5 Feb (Wed)		\| \| [[CDS 140a Winter 2014 Homework 4\|HW 4]] <br> Due: 5 Feb (Wed)
	\|- valign=top		\|- valign=top
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	* Center manifold theorem		* Center manifold theorem
	\| Perko, 2.11-2.13		\| 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)]]
	~~-->~~
	\| [[CDS 140a Winter 2014 Homework 5\|HW 5]] <br> Due: 12 Feb (Wed)		\| [[CDS 140a Winter 2014 Homework 5\|HW 5]] <br> Due: 12 Feb (Wed)
	\|- valign=top		\|- valign=top
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	\| 25 Feb <br> 27 Feb		\| 25 Feb <br> 27 Feb
	\| Bifurcations		\| Bifurcations
			* Sensitivity analysis
	* Structural stability		* Structural stability
	* Bifurcation of equilibrium points		* Bifurcation of equilibrium points
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	\| 4 Mar <br> 6 Mar		\| 4 Mar <br> 6 Mar
	\| Bifurcations		\| Bifurcations
	* Higher co-dimension bifurcations
	* Hopf bifurcation		* Hopf bifurcation
	* Hamiltonian systems (if time)
	\| Perko 4.3-4.5 + notes		\| Perko 4.3-4.5 + notes
	\| [[CDS 140a Winter 2014 Homework 9\|HW 9]] <br> Due: 12 Mar (Wed)		\| [[CDS 140a Winter 2014 Homework 9\|HW 9]] <br> Due: 12 Mar (Wed)

Murray: /* Lecture Schedule */

2014-03-12T05:50:47Z

Lecture Schedule

← Older revision		Revision as of 05:50, 12 March 2014
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	\| Course review		\| Course review
	\| <!-- Reading -->		\| <!-- Reading -->
	\| Final exam <br> Due: 19 Mar (Wed)~~<br>~~		\| Final exam <br> Due: 19 Mar (Wed). Pick up from Diane Goodfellow, 246 ANB
	Pick up from Diane Goodfellow, 246 ANB
	\|}		\|}

Murray: /* Lecture Schedule */

2014-03-12T05:50:16Z

Lecture Schedule

← Older revision		Revision as of 05:50, 12 March 2014
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	\| Course review		\| Course review
	\| <!-- Reading -->		\| <!-- Reading -->
	\| Final exam <br> Due: 19 Mar (Wed)		\| Final exam <br> Due: 19 Mar (Wed)<br>
			Pick up from Diane Goodfellow, 246 ANB
	\|}		\|}

Murray: /* Lecture Schedule */

2014-02-23T17:27:20Z

Lecture Schedule

← Older revision		Revision as of 17:27, 23 February 2014
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	* Bifurcation of equilibrium points		* Bifurcation of equilibrium points
	\| 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]
	\| [[CDS 140a Winter 2014 Homework 8\|HW 8]] <br> Due: 5 Mar (Wed)		\| [[CDS 140a Winter 2014 Homework 8\|HW 8]] <br> Due: 5 Mar (Wed)
	~~<!--~~
	* [http://www.cds.caltech.edu/~murray/courses/cds140/wi11/caltech/L8-1_bfs_sensitivity.pdf BFS notes on parameter sensitivity]
	~~-->~~
	\|- valign=top		\|- valign=top
	\| 4 Mar <br> 6 Mar		\| 4 Mar <br> 6 Mar

Murray: /* Announcements */

2014-02-17T04:28:22Z

Announcements

← Older revision		Revision as of 04:28, 17 February 2014
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	=== Course Description ===		=== 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.		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 ===~~

	* 29 Dec 2013: updated course information
	* 4 Nov 2013: web page creation

	=== Lecture Schedule ===		=== Lecture Schedule ===

Murray at 04:28, 17 February 2014

2014-02-17T04:28:10Z

← Older revision		Revision as of 04:28, 17 February 2014
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	* Katie Broersma (CDS), Anandh Swaminathan (CDS)		* Katie Broersma (CDS), Anandh Swaminathan (CDS)
	* Contact: cds140-tas@cds.caltech.edu		* Contact: cds140-tas@cds.caltech.edu
	* Office hours: Tue, 3:30-4:30, 101 STH		* Office hours: Tue, 3:00-4:30, 101 STH
	\|}		\|}

Murray at 04:27, 17 February 2014

2014-02-17T04:27:58Z

← Older revision		Revision as of 04:27, 17 February 2014
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	\| width=50% \|		\| width=50% \|
	'''Teaching Assistants'''		'''Teaching Assistants'''
	* Katie Broersma (CDS), ~~Vanessa Jonsson~~ (CDS)		* Katie Broersma (CDS), Anandh Swaminathan (CDS)
	* Contact: cds140-tas@cds.caltech.edu		* Contact: cds140-tas@cds.caltech.edu
	* Office hours: Tue, 3:30-4:30, 101 STH		* Office hours: Tue, 3:30-4:30, 101 STH

Murray: /* Lecture Schedule */

2014-02-02T22:33:08Z

Lecture Schedule

← Older revision		Revision as of 22:33, 2 February 2014
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	\|- valign=top		\|- valign=top
	\| 11 Feb <br> 13 Feb		\| 11 Feb <br> 13 Feb
	\| ~~Hamiltonian systems~~		\| Global behavior
	* ~~Gradient~~ and ~~Hamiltonian systems~~		* Limit sets and attractors
	* ~~Energy based stability methods~~		* Krasovskii-Lasalle invariance principle (if time)
	* ~~Applications~~		* Periodic orbits and limit cycles
	\| Perko ~~2.14 + notes~~		\| Perko, 3.1-3.3
	~~<!--~~
	* [http://www.cds.caltech.edu/~macmardg/courses/cds140a/L6-Hamiltonian.pdf Scanned lecture notes]
	* [http://www.cds.caltech.edu/~macmardg/courses/cds140a/MarsdenMechSystems.pdf Marsden, ~~Mechanical systems]~~
	* [[Media:cds140a-wi11-Week6NotesHamGrad.~~pdf\|Gradient and Hamiltonian Systems]]~~
	* [[Media:cds140a-wi11-~~Week6NotesLagHamSum~~.~~pdf\|Lagrangian, Summary]]~~
	~~-->~~
	\| [[CDS 140a Winter 2014 Homework 6\|HW 6]] <br> Due: 19 Feb (Wed)		\| [[CDS 140a Winter 2014 Homework 6\|HW 6]] <br> Due: 19 Feb (Wed)
	\|- valign=top		\|- valign=top
	\| 18 Feb* <br> 20 Feb* ~~<br> 25 Feb~~		\| 18 Feb* <br> 20 Feb*
	\| Limit cycles		\| Limit cycles
	* Limit sets and attractors
	* Periodic orbits and limit cycles
	* Poincare' map		* Poincare' map
	* Bendixson criterion for limit cycles in the plane		* Bendixson criterion for limit cycles in the plane
	\| Perko, 3.1-3.5, 3.7~~, 3.9~~		\| Perko, 3.4-3.5, 3.7
	~~<!--~~		\| [[CDS 140a Winter 2014 Homework 7\|HW 7]] <br> Due: 26 Feb (Wed)
	* [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 2014 Homework 7\|HW 7]] <br> Due: ~~5 Mar~~ (Wed)
	\|- valign=top		\|- valign=top
	\|~~- valign=top~~		\| 25 Feb <br> 27 Feb
	~~\| 27~~ Feb <br> ~~4 Mar <br> 6 Mar~~
	\| Bifurcations		\| Bifurcations
	* Structural stability		* Structural stability
	* Bifurcation of equilibrium points		* Bifurcation of equilibrium points
	* Hopf bifurcation		\| Perko 4.1-4.2 + notes
	\| Perko 4.1-4.4 + notes		\| [[CDS 140a Winter 2014 Homework 8\|HW 8]] <br> Due: 5 Mar (Wed)
	<!--		<!--
	* [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/L8-1_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 2014 Homework 8\|HW 8]] <br> Due: 12 Mar (Wed)		\|- valign=top
			\| 4 Mar <br> 6 Mar
			\| Bifurcations
			* Higher co-dimension bifurcations
			* Hopf bifurcation
			* Hamiltonian systems (if time)
			\| Perko 4.3-4.5 + notes
			\| [[CDS 140a Winter 2014 Homework 9\|HW 9]] <br> Due: 12 Mar (Wed)
	\|- valign=top		\|- valign=top
	\| 11 Mar* <br>		\| 11 Mar* <br>

Murray: /* Lecture Schedule */

2014-01-27T02:18:28Z

Lecture Schedule

← Older revision		Revision as of 02:18, 27 January 2014
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	\| Behavior of differential equations		\| Behavior of differential equations
	* Stable and unstable manifolds		* Stable and unstable manifolds
	* Stability of equilibrium points		* Stability of equilibrium points for planar systems
	\| Perko, 2.7-2.10		\| Perko, 2.7-2.10
	<!--		<!--