MATH538: Techniques of Applied Mathematics

Location and Time

LEC R1: TR 1100-1220 Location CAB563

Midterm

Worth 30% of final grade (unless Final Exam has better grade)

Where and when: 11:00-12:20 in class on Thurs. Feb 16

Exam

Worth 30% of final grade (or worth 60% if this is better than 30% midterm and 30% exam combined.)

Where and when: 9:00-noon on Wed. Apr 19 in CAB563

Assignments

Worth 40% of final grade

4 assignments total, each worth equal weight.

Assignment 1: Due 6pm Friday, January 27   Solutions to Assignment 1

Assignment 2: Due 6pm Friday, February 10   Solutions to Assignment 2

Assignment 3: Due 3pm Tuesday, March 21   Solutions to Assignment 3

Assignment 4: Due 3pm Tuesday, April 11  

Syllabus

You can download the syllabus.

Extra Help

Office Hours: by appointment (within 24 hours guaranteed)

Overheads and Handouts

Here are some math tricks that often come in handy.

Course Outline

Continuation of asymptotic expansion of integrals, perturbation theory, asymptotic matching, perturbative eigenvalue problems, boundary layer theory, WKB theory.

Textbook

For the most part, the course will follow the material in the recommended but not required textbook

Applied Mathematics, 2nd Ed.,
J. David Logan, J. Wiley and Sons Pub.

Other recommended resources

• Course lecture notes
  1. Dimensional Analysis: Buckingham PI Theory
  2. Dimensional Analysis: Converting PDEs to ODEs
  3. Scaling Theory: Nondimensionalization of DEs
  4. Perturbation Theory: Polynomials
  5. Perturbation Theory: Matrix Eigenvalue Problems
  6. Perturbation Theory: Initial Value Problems for DEs
  7. Perturbation Theory: Boundary Layer Theory for DEs
  8. Perturbation Theory: Differential Eigenvalue Problems
  9. Perturbation Theory: Linear Stability Theory
  10. Perturbation Theory: Bifurcation Theory
  11. Perturbation Theory: WKB Theory
  12. Perturbation Theory: More WKB - Ray Theory
  13. Asymptotic Approximation of Integrals: Integration by Parts
  14. Asymptotic Approximation of Integrals: Laplace Transforms
  15. Asymptotic Approximation of Integrals: Generalized Fourier Integrals
  16. Series: Inversion and Accelerated Convergence
  17. Series: Divergent Sums

• Advanced Mathematical Methods for Scientists and Engineers,
  Bender and Orszag, Springer-Verlag Pub.
  

• Pertubation Theory,
  Lister, Cambridge University Press
  

Prerequisites

MATH 438, or consent of instructor

Department of Mathematical Sciences home page