MATH 501: Analytic Methods in Applied Mathematics

Welcome to the course webpage for Math 501! This course is offered to graduate students at Cal Poly, and discusses asymptotics and perturbation techniques in order to solve timely problems in Applied Mathematics. In particular, we will discuss approximation methods for solving ODEs, regular and singular perturbation theory, boundary layer theory, WKB expansions and applications to eigenvalue problems, as well as multiple-scale techniques. Please visit the Canvas page for this course for more information and announcements.

Course Instructor: Dr. Stathis Charalampidis

SC's Office Hours: TR: 11:15am-12:45pm, or by appointment
Class Meetings:

  • TR 7:10-9:00am (38-148)
Required Textbook:
  • Advanced Mathematical Methods for Scientists and Engineers I (Asymptotic Methods and Perturbation Theory), Authors: Carl M. Bender and Steven A. Orszag, Publisher: Springer-Verlag.
Additional References:
  • Perturbation Methods, Authors: John Hinch, Publisher: Cambridge Press.
  • Introduction to Perturbation Methods, Authors: Mark H. Holmes, Publisher: Springer-Verlag.
  • Introduction to the Calculus of Variations, Author: Bernard Dacorogna, Publisher: Imperial College Press.

Class Material by Topic:

  • Local Analysis of linear and nonlinear ODEs
  • Perturbation series for ODEs and eigenvalue problems
  • Boundary layer theory
  • Wentzel–Kramers–Brillouin (WKB) theory
  • Multiple-scale analysis
Syllabus and Tentative Schedule:

Please click here for the complete course syllabus.

Homework Assignments:

Please visit the Canvas page for the course for a complete list of homework assignments.

Academic Calendar:

For your convenience, links for the academic calendar are included in this section: