Asymptotics and Perturbation Methods
Asymptotics and Perturbation Methods (Spring 2021). Instructor: Prof. Steven Strogatz, Department of Mathematics, Cornell University. Asymptotic methods and perturbation theory are clever techniques for finding approximate analytical solutions to complicated problems, by exploiting the presence of a large or small parameter. This course is an introduction to such methods and their applications in various branches of science and engineering. The prerequisites are a knowledge of basic calculus and differential equations at an undergraduate level. The course emphasizes concrete examples, intuition, and applications to science and engineering, rather than theorems, proofs, and mathematical rigor. The treatment is friendly yet careful. Topics include asymptotic expansion of integrals via Laplace's method, stationary phase, steepest descent, and saddle points. Perturbation methods for differential equations include dominant balance, boundary layer theory, multiple scales, and WKB theory. Most of the examples in the course deal with integrals or ordinary differential equations, but if time permits, we might also discuss some applications involving partial differential equations and difference equations.
| Asymptotic Expansions |