CDS 140, Winter 2016
Line 21:  Line 21:  
* Homework will be due Wednesdays in class (or by 5pm to Benson). HW 1 is posted below.  * Homework will be due Wednesdays in class (or by 5pm to Benson). HW 1 is posted below.  
* [https://piazza.com/caltech/winter2016/cds140/home Piazza] If you have not received an email to sign up for Piazza, please email us!  * [https://piazza.com/caltech/winter2016/cds140/home Piazza] If you have not received an email to sign up for Piazza, please email us!  
+  * Dates for recitation are shown in italics in schedule. Dates where JCD is lecturing given with asterisk  
=== Course Description ===  === Course Description ===  
Line 35:  Line 36:  
 valign=top   valign=top  
 valign=top   valign=top  
−   4 Jan <br> 6 Jan  +   4 Jan <br> 6 Jan <br> ''8 Jan'' 
 Linear Differential Equations [http://www.cds.caltech.edu/~macmardg/courses/cds140a/wi16/L11.pdf L11] [http://www.cds.caltech.edu/~macmardg/courses/cds140a/wi16/LinearSystemsNotes.pdf LinSys notes]   Linear Differential Equations [http://www.cds.caltech.edu/~macmardg/courses/cds140a/wi16/L11.pdf L11] [http://www.cds.caltech.edu/~macmardg/courses/cds140a/wi16/LinearSystemsNotes.pdf LinSys notes]  
* Course overview and administration  * Course overview and administration  
Line 46:  Line 47:  
 [http://www.cds.caltech.edu/~macmardg/courses/cds140a/wi16/hw1wi16.pdf hw1wi16.pdf] <br> Due: 13 Jan (Wed)   [http://www.cds.caltech.edu/~macmardg/courses/cds140a/wi16/hw1wi16.pdf hw1wi16.pdf] <br> Due: 13 Jan (Wed)  
 valign=top   valign=top  
−   11 Jan <br> 13  +   11 Jan <br> 13 Jan <br> ''15 Jan'' 
 Nonlinear differential equations   Nonlinear differential equations  
* Existence and uniqueness  * Existence and uniqueness  
Line 54:  Line 55:  
 [[CDS 140a Winter 2016 Homework 2HW 2]] <br> Due: 20 Jan (Wed)   [[CDS 140a Winter 2016 Homework 2HW 2]] <br> Due: 20 Jan (Wed)  
 valign=top   valign=top  
−   20 Jan <br> 22 Jan  +   20 Jan* <br> 22 Jan* 
 Behavior of differential equations   Behavior of differential equations  
* Stable and unstable manifolds  * Stable and unstable manifolds  
Line 61:  Line 62:  
 [[CDS 140a Winter 2016 Homework 3HW 3]] <br> Due: 27 Jan (Wed)   [[CDS 140a Winter 2016 Homework 3HW 3]] <br> Due: 27 Jan (Wed)  
 valign=top   valign=top  
−   25 Jan <br>  +   25 Jan <br> '''(2 hr?)''' <br> ''Jan 29'' 
 Nonhyperbolic differential equations   Nonhyperbolic differential equations  
* Lyapunov functions  * Lyapunov functions  
Line 68:  Line 69:  
 [[CDS 140a Winter 2016 Homework 4HW 4]] <br> Due: 3 Feb (Wed)   [[CDS 140a Winter 2016 Homework 4HW 4]] <br> Due: 3 Feb (Wed)  
 valign=top   valign=top  
−    +   1 Feb* <br> 3 Feb* <br> 5 Feb* 
 Global behavior   Global behavior  
* Limit sets and attractors  * Limit sets and attractors  
Line 76:  Line 77:  
 [[CDS 140a Winter 2016 Homework 5HW 5]] <br> Due: 10 Feb (Wed)   [[CDS 140a Winter 2016 Homework 5HW 5]] <br> Due: 10 Feb (Wed)  
 valign=top   valign=top  
−    +   8 Feb <br> 10 Feb <br> 12 Feb 
 Limit cycles   Limit cycles  
* Poincare' map  * Poincare' map  
Line 84:  Line 85:  
 [[CDS 140a Winter 2016 Homework 6HW 6]] <br> Due: 17 Feb (Wed)   [[CDS 140a Winter 2016 Homework 6HW 6]] <br> Due: 17 Feb (Wed)  
 valign=top   valign=top  
−    +   15 Feb <br> 17 Feb <br> 19 Feb 
 Bifurcations   Bifurcations  
* Sensitivity analysis  * Sensitivity analysis  
Line 93:  Line 94:  
 [[CDS 140a Winter 2016 Homework 7HW 7]] <br> Due: 24 Feb (Wed)   [[CDS 140a Winter 2016 Homework 7HW 7]] <br> Due: 24 Feb (Wed)  
 valign=top   valign=top  
−    +   22 Feb <br> 24 Feb* <br> 26 Feb? 
 Bifurcations   Bifurcations  
* Hopf bifurcation  * Hopf bifurcation  
Line 100:  Line 101:  
 [[CDS 140a Winter 2016 Homework 8HW 8]] <br> Due: 2 Mar (Wed)   [[CDS 140a Winter 2016 Homework 8HW 8]] <br> Due: 2 Mar (Wed)  
 valign=top   valign=top  
−   2 Mar <br>  +   29 Feb <br> 2 Mar <br> 4 Mar 
 Nonlinear control systems   Nonlinear control systems  
 {{obc08OBC}}, Chapter 1   {{obc08OBC}}, Chapter 1  
 OBC 1.3, 1.4ab, 1.5<br> Due: 9 Mar (Wed)   OBC 1.3, 1.4ab, 1.5<br> Due: 9 Mar (Wed)  
 valign=top   valign=top  
−   9 Mar <br>  +   7, 9 Mar <br> 
 Course review   Course review  
 <! Reading >   <! Reading > 
Revision as of 01:05, 6 January 2016
Introduction to Dynamics  
Instructors

Teaching Assistants

Announcements
 Homework will be due Wednesdays in class (or by 5pm to Benson). HW 1 is posted below.
 Piazza If you have not received an email to sign up for Piazza, please email us!
 Dates for recitation are shown in italics in schedule. Dates where JCD is lecturing given with asterisk
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, PoincaréBendixon theory, Poincaré maps. Introduction to simple bifurcations, including Hopf bifurcations, invariant and center manifolds.
Lecture Schedule
Date  Topic  Reading  Homework 
4 Jan 6 Jan 8 Jan 
Linear Differential Equations L11 LinSys notes

Perko, 1.11.10 
hw1wi16.pdf Due: 13 Jan (Wed) 
11 Jan 13 Jan 15 Jan 
Nonlinear differential equations

Perko, 2.12.6  HW 2 Due: 20 Jan (Wed) 
20 Jan* 22 Jan* 
Behavior of differential equations

Perko, 2.72.10  HW 3 Due: 27 Jan (Wed) 
25 Jan (2 hr?) Jan 29 
Nonhyperbolic differential equations

Perko, 2.112.13  HW 4 Due: 3 Feb (Wed) 
1 Feb* 3 Feb* 5 Feb* 
Global behavior

Perko, 3.13.3  HW 5 Due: 10 Feb (Wed) 
8 Feb 10 Feb 12 Feb 
Limit cycles

Perko, 3.43.5, 3.7  HW 6 Due: 17 Feb (Wed) 
15 Feb 17 Feb 19 Feb 
Bifurcations

Perko 4.14.2 
HW 7 Due: 24 Feb (Wed) 
22 Feb 24 Feb* 26 Feb? 
Bifurcations

Perko 4.34.5 + notes  HW 8 Due: 2 Mar (Wed) 
29 Feb 2 Mar 4 Mar 
Nonlinear control systems  Template:Obc08, Chapter 1  OBC 1.3, 1.4ab, 1.5 Due: 9 Mar (Wed) 
7, 9 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:
[G&H]  J. Guckenheimer and P. Holmes, Nonlinear oscillations, dynamical systems, and bifurcations of vector fields. SpringerVerlag, 1990. 
[H&S]  M. Hirsch and S. Smale, Differential Equations, Dynamical Systems, and Linear Algebra. SpringerVerlag, 1990. 
[J&S]  D. Jordan and P. Smith, Nonlinear Ordinary Differential Equations: An Introduction for Scientists and Engineers, Fourth Edition. Oxford University Press, 2007. (On reserve in SFL) 
[Ver]  F. Verhulst, Nonlinear Differential Equations and Dynamical Systems, Second Edition. Springer, 2006. (On reserve in SFL) 
Grading
The ﬁnal grade will be based on homework and a ﬁnal exam:
 Homework (75%)  There will be 9 oneweek 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 48N 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.