Math 204: Applied Asymptotic Analysis

Course Request Summary

Department Submitting Request: Mathematics

Request for Action: CHANGE   Effective: 200210

Course Subject Area: Mathematics

Subject Code: MAT Course Number: 204

Descriptive Title: Applied Asymptotic Analysis

Abbreviated Title: Asymptotic Analysis

Units: 4

Learning Activity

1st LEC 3.0 hrs/wk

2nd T-D 1.0 hrs/wk

In Progress Grading: None

Instructor Consent:

Prerequisite(s): Graduate standing or consent of instructor.

Restrictions on Enrollment:

Course Description: Scaling and non-dimensionalization. Asymptotic expansions. Regular and singular perturbation methods. Applications to algebraic and ordinary and partial differential equations in the natural sciences and engineering.

  General Education: No GE Certification

     Topical Breadth:

                 Diversity:

Writing Experience:

Cross Listing: Same Course as

Repeat Credit:

Credit Limitations:

Mode of Grading: Letter

Quarters to be Offered: I Alternate Years

Instructors Name(s): Staff - Chair in Charge Title(s):

Remarks:
New course description more accurately reflects course content.

Expanded Course Description

1. COURSE GOALS:
   Developing formal manipulation skills with algebraic and differential equations; learning the basics of mathematical modeling, scaling and dimensional analysis; learning how to use perturbation and asymptotic series methods to find analytical approximate solutions of algebraic and differential equations.
   
2. ENTRY LEVEL:
   Graduate standing or consent of instructor.
3. TOPICAL OUTLINE:
   Regular perturbation method for ODEs.
   Poincare-Linstedt method for ODEs.
   Singular perturbations: boundary layer analysis.
   Asymptotic series and expansions.
   Asymptotic expansion of integrals.
   Finding roots of polynomial equations using scaling and perturbation theory.
   WKB method.
   Methods of steepest descent and stationary phase.  
4. READING:
   Logan, J. D. (1997). Applied mathematics. New York, Wiley.
   Lin, C. C. and L. A. Segel (1988). Mathematics applied to deterministic problems in the natural sciences. Philadelphia, Siam.
   Murray, J. D. (1984). Asymptotic analysis. New York, Springer-Verlag.
   
5. GRADING PERCENTAGES AND COURSE REQUIREMENTS:
   Homework problem assignments 50 %
   Take home final exam 30 %
   Term paper 20 %
   
6. EXPLANATION OF POTENTIAL COURSE OVERLAP:
   None
7. GENERAL EDUCATION DESIGNATION:
   None