I'm teaching a course on asymptotics and perturbation methods, and thought it might be fun to share the lectures on @YouTube. Here's lecture 1, which introduces the idea of asymptotic expansions. (For more about the course, see the rest of this thread.)
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.
The prerequisites are a knowledge of 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 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.
For those of you following the course on asymptotics and perturbation methods, please consider subscribing to my YouTube channel. I will be posting lectures every Tuesday and Thursday.
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