Revised January 31, 2007 to reflect renumbering of undergraduate prerequisites.

 

Course Request Summary

 

Department Submitting Request: Mathematics

Request for Action: CHANGE

Effective: 200710

Course Subject Area: Mathematics

Subject Code: MAT

Course Number: 219

Descriptive Title: Ordinary Differential Equations

Abbreviated Title: Ord. Diff. Equations

Units: 4

 

 

Learning Activity

1st LEC 3.0 hrs/wk

2nd T-D 1.0 hrs/wk

 

In Progress Grading: None

Consent of Instructor: No

Prerequisite(s): Course 22A or 67, 22B, 125B or consent of instructor

Restrictions on Enrollment:

Course Description: Theory of ordinary differential equations. Dynamical systems. Geometric theory. Normal forms. Bifurcation theory. Chaotic systems.

General Education: No GE Certification

Topical Breadth:

Diversity:

Writing Experience:

Cross Listing: Same Course as

Justification:

Repeat Credit: No

 

Credit Limitations:

Mode of Grading: Letter

Quarters to be Offered: I Alternate Years

Instructors Name(s): Staff, Chair in Charge

Title(s):

 

Remarks:

Change of prerequisites due to change in our undergraduate courses and degree requirements. Math 127C is canceled. The material from 127C will now be Math 125B. Also, we will offer a new class: Math 67, Advanced Linear Algebra.

 

 

 

 

Expanded Course Description

 

TOPICAL OUTLINE:

Existence and uniqueness theorems for ordinary differential equations. Dynamical systems and the geometric theory of ordinary differential equations. Normal forms and bifurcation theory. Chaotic dynamical systems. Applications.

 

READING:

Text:

  • S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos (Texts in Applied Mathematics, Vol. 2), Springer-Verlag, 19990.

 

Other Readings:

  • V.I. Arnold, Ordinary Differential Equations
  • M.W. Hirsch and S. Smale, Differential Equations, Dynamical Systems and Linear Algebra
  • J. Gukenheimer and P.Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields
  • E.A. Coddington and N. Levinson, Theory of Ordinary Differential Equations
  • J. Hale, Ordinary Differential Equations
  • P.Hartman, Ordinary Differential Equations

 

GRADING PERCENTAGES:

 

COURSE FORMAT AND REQUIREMENTS:

The instructor has a choice of how he or she would like to run the class: (1) Student workload is 3 hours of lecture, 6 hours of outside preparation, and 3 hours of term paper research and writing for a total of 12 hours per week; or (2) Student workload is 3 hours of lecture, 1 hours of discussion, and 8 hours of outside preparation for a total of 12 hours per week.

 

EXPLANATION OF POTENTIAL COURSE OVERLAP:

None.

 

GENERAL EDUCATION JUSTIFICATION:

N/A

 

ADDITIONAL INFORMATION FOR STUDENTS:

 

 

 

 

 

Old Information

 

COURSE GOALS:

To provide a graduate level description of the theory of ordinary differential equations and dynamical systems.

 

ENTRY LEVEL:

Graduate standing or consent of instructor.