Applied Analysis – 4525

Course Number: 4525
Credits: 4
Description: Demonstrates the applications of mathematics to interesting physical and biological problems. Methods are chosen from ordinary and partial differential equations, calculus of variations, Laplace transform, perturbation theory, special functions, dimensional analysis, asymptotic analysis, and other techniques of applied mathematics.

Dimensional Analysis and Scaling
– Buckingham Pi Theorem
– Method of Scaling
Perturbation Methods
– Regular Perturbation Method
– Poincaré-Lindstedt Method
– Method of Multiple Scales
– WKB Method
– Boundary Layer Method
Calculus of Variations
– Function Spaces and Functionals
– Euler-Lagrange Equations
– Constraints

– Logan Applied Mathematics
– Simmonds-Mann Jr. A First Look at Perturbation Theory
– Kot A First Course in the
Calculus of Variations