CDS 140b, Spring 2014
Differential Equations and Dynamical Systems  
Instructors

Teaching Assistants

Course Description
CDS 140b is a continuation of CDS 140a. A large part of the course will focus on tools from nonlinear dynamics, such as perturbation theory and averaging, advanced stability analysis, the existence of periodic orbits, bifurcation theory, chaos, etc. In addition, guest lecturers will give an introduction to current research topics in dynamical systems theory. There will be 5 homeworks throughout the term but no exams. Instead, the students are required to select a research topic and a journal paper related to CDS140b and present a brief review of the paper. The details of the projects will be discussed in the class.
Lecture Schedule
Week  Date  Topic  Suggested Reading/Lecture Notes  Homework 
0  31 Mar RMM 
Course overview  
1  2 Apr 4 Apr* DGM 
Lagrangian and Hamiltonian systems I


HW 1 Due: 9 Apr (Wed) 
2  9 Apr* 11 Apr DGM 
Lagrangian and Hamiltonian systems II

Perko 3.6  HW 2 
3  18 Apr 21 Apr RMM 
Advanced stability theory


HW 3 
4  28 Apr 30 Apr RMM 
Perturbation Theory


HW 4 
5  5 May 7 May RMM 
Averaging Method


HW 5 
6  12 May 14 May RMM 
Singular Perturbations


HW 6 
7  21 May 23 May* DGM 
Nonlinear control I


HW 7 
8  28 May 30 May DGM 
Nonlinear control II


HW 8 
9  2 Jun 3 Jun 
Project presentations 
References:
Course Textbooks
 H. Khalil, Nonlinear Systems, Prentice Hall; 3rd edition, 2001. ISBN: 9780130673893
 S. Strogatz, Nonlinear Dynamics And Chaos, Westview Press, 1994. ISBN: 9780738204536
 F. Verhulst, Nonlinear Differential Equations and Dynamical Systems, Springer; 2ed Edition, 1996. ISBN: 9783540609346
Additional Sources:
 L. Perko, Differential Equations and Dynamical Systems (3rd), Springer, 2001. ISBN: 9780387951164
 S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer; 2nd edition, 2003. ISBN: 9780387001777
Policies
Collaboration Policy
Homeworks are to be done and handed in individually. To improve the learning process, students are encouraged to discuss the problems with, provide guidance to and get help from other students, the TAs and instructors. However, to make sure each student understands the concepts, solutions must be written independently and should reﬂect your understanding of the subject matter at the time of writing. Copying solutions, using solutions from previous years, having someone else type or dictate any part of the solution manual or using publicly available solutions (from the Internet) are not allowed.
Grading Policy
The final grades will be evaluated based on homework assignments (75%) and final projects (25%).
Late Homework
Each student is allowed one late day which means only one homework assignment may be handed in up to one day late. Other than this day, late homework will not be accepted. Exceptional circumstances (such as medical situations) with appropriate documentation will be considered by the instructors.
Projects
TBD