Lecture Notes on Asymptotic Analysis

By Tiejun Li

The aim of this course is to teach the students the basic asymptotic analysis techniques. Only the asymptotic analysis for ODEs are discussed since it is aimed to second year undergrad students. The students are assumed to have the basic knowledge about the ODEs and complex analysis.



Lect01 Introduction

Asymptotics for Integrals

Lect02 Laplace Methods ( Homework 01)

Lect03 Stationary Phase Approximation ( Homework 02)

Lect04 Method of Steepest Descent ( Homework 03)

Lect05 Asymptotics for Sums ( Homework 04)

Local Analysis

Lect06 ODE Review ( Homework 05, Homework 06)

Lect07 ODE I: Ordinary and regular singular point (Homework 07)

Lect08 ODE II: Irregular singular point (Homework 08)

Lect09 Asymptotic series (Homework 09)

Lect10 Nonlinear ODEs: I (Homework 10)

Lect11 Nonlinear ODEs: II (Homework 11)

Global Analysis

Lect12 Perturbation Theory: Basics (Homework 12)

Lect13 Asymptotic Matching (Homework 13)

Lect14 Boundary Layer Theory: I (Homework 14)

Lect15 Boundary Layer Theory: II (Homework 15)

Lect16 WKB Asymptotics: I (Homework 16)

Lect17 WKB Asymptotics: II (Homework 17)

Lect18 Multiscale Analysis: I (Homework 18)

Lect19 Multiscale Analysis: II (Homework 19)