ACM 101/AM 125b/CDS 140a, Winter 2013

Differential Equations and Dynamical Systems  
Instructors

Teaching Assistants

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.
Announcements
 16 Dec 2012: set up Piazza page + added additional course info
 23 Aug 2012: web page creation
Lecture Schedule
Date  Topic  Reading  Homework 
8 Jan 10 Jan RMM 
Linear Differential Equations I

Perko, 1.11.6

HW 1 Due: 15 Jan (Tue) 
15 Jan 17 Jan RMM 
Linear Differential Equations II

Perko, 1.71.10 + notes  HW 2 Due: 22 Jan (Tue) 
22 Jan 24 Jan RMM 
Nonlinear differential equations

Perko, 2.12.6  HW 3 Due: 29 Jan (Tue) 
29 Jan* 31 Jan DGM 
Behavior of differential equations

Perko, 2.72.10  HW 4 Due: 5 Feb (Tue) 
5 Feb* 7 Feb DGM 
Nonhyperbolic differential equations

Perko, 2.112.13  HW 5 Due: 12 Feb (Tue) 
12 Feb 14 Feb* DGM 
Hamiltonian systems

Perko 2.14 + notes  HW 6 Due: 19 Feb (Tue) 
19 Feb 21 Feb* 26 Feb RMM 
Limit cycles

Perko, 3.13.5, 3.7, 3.9  HW 7 Due: 5 Mar (Tue) 
28 Feb 5 Mar 7 Mar* RMM 
Bifurcations

Perko 4.14.4 + notes  HW 8 Due: 12 Mar (Tue) 
12 Mar 
Course review 
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 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.
No collaboration is allowed on the ﬁnal exam.