MATH 558 Methods of Applied Mathematics, Fall 2018

A NetMath project

Instructor  Vera Mikyoung Hur
Class meets  TR 9:30-10:50am in 343 Altgeld Hall
Office hours  Wednesday 9:30am-12:30pm in 269 Altgeld Hall, or by appointments.

Lecture notes and videos

Dimensional Analysis

Mark H. Holmes Introduction to the Foundations of Applied Mathematics, Chapter 1. Free access from Illinois networks.
See also
G. I. Barenblatt Scaling, Self-similarity, and Intermediate Asymptotics, Chapters 1-2.

Table of fundamental dimensions for commonly occurring quantities
Abramowitz and Stegun

Dimensional reduction notes video
Buckingham pi theorem, nondimensionalization notes
Self-similar solutions notes video
Example: atomic explosion notes video

Asymptotic Approximations

Mark H. Holmes Introduction to the Foundations of Applied Mathematics, Chapter 2.
Mark H. Holmes Introduction to Perturbation Methods, Chapters 2. Free access from Illinois networks.

Introduction to asymptotic approximations notes video
Matched asymptotic expansions notes video
Multiple boundary layers notes video

Multiple Scales

Mark H. Holmes. Introduction to Perturbation Methods, Chapter 3.

Reiss example notes video
Three time scales and two term expansion notes video
Forced motion near resonance notes video video
Slowly varying coefficients notes video

WKB Method

Mark H. Holmes. Introduction to Perturbation Methods, Chapter 4.

Introductory example notes video
Turning point notes video
Wave propagation and energy method notes video

Dispersive Waves

G. B. Whitham. Linear and Nonlinear Waves, Chapter 11.

Dispersive waves notes video
Method of stationary phase and group velocity notes video
Kinematic derivation and energy method notes video
Variational approach notes video

Bifuriocation and Stability

Mark H. Holmes. Introduction to Perturbation Methods, Chapter 6.

Bifurcation condition and Lyapunov-Schmidt method notes video
Lyapunov-Schmidt continued and stability