## 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