Lecture Recordings

Lecture 16

Summary.

  • Method of Matched Asymptotic Expansions

  • Dimensionless parameters

Lecture 15

Summary.

  • Method of Matched Asymptotic Expansions

Lecture 14

Summary.

  • Stirling’s approximation

Lecture 13

Summary.

  • Laplace’s method

Lecture 12

Summary.

  • Asymptotic approximations of integrals

  • Examples

  • Introduction to Laplace’s method

Lecture 11

Summary.

  • Lindstedt-Poincare method

  • Introducing an unknown frequency of periodic solutions

  • Using the unknown frequency to eliminate secular terms

Lecture 10

Summary.

  • Duffing’s equation

  • Seeking a solution via a straightforward approach

  • Encountering a secular term

Lecture 09

Summary.

  • Mass on a non-linear spring

  • Conservation of mechanical energy

  • Introduction of a small parameter

Lecture 08

Summary.

  • Kruskal-Newton graphs

Lecture 07

Summary.

  • Singular perturbation ansatz

  • Dominant balance (a more complicated example)

Lecture 06

Summary.

  • Singular perturbation ansatz

  • Dominant balance

Lecture 05

Summary.

  • Regularly perturbed ODE

  • Singularly perturbed algebraic equation

Lecture 04

Summary.

  • Operations with Landau symbols

  • Integration and differentiation

  • Asymptotic sequences

  • Asymptotic expansions

Lecture 03

Summary.

  • Big \(O\) examples

  • Little \(o\)

  • Asymptotic equivalence (\(\sim\))

Lecture 02

Summary.

  • Landau symbols

  • Big \(O\)

  • Example

Lecture 01

Summary.

  • How the module works

  • Why study asymptotic methods?

  • Introduction - a toy example approximating a root of a quadratic equation