# MATH 451

## Announcements

• For a general overview of the course, download the Course Policies given below.
• The FINAL EXAM is 4-5:50pm on Monday, May 5.

Course Policies: PDF

Textbook: Applied Mathematics, by J. David Logan (2nd edition)

## Topics for the Course

1. Chapter 3: Calculus of Variations
• Calculus and Function Space Background
• Simplest Problem in CoV
• Euler-Lagrange DE
• Hamilton's Principle
• Isoperimetric Problems
2. Chapter 6: Partial Differential Equation Models
• Multivariable Calculus Background
• Conservation Laws and Constitutive Equations
• Equilibrium Equations
• Diffusion Equations
• Fourier Series (from Chap 4)
• (Regular) Sturm Liouville Problems (from Chap 4)
• Separation of Variables
• Laplace and Fourier Transforms
3. Chapter 4: Eigenvalue Problems, Integral Equations and Green's Functions
• Regrettably, I didn't have time to cover Green's Functions
• Most regrettably, I didn't cover Distributions
4. Chapter 7: Wave Phenomena

## Homework Assignments

• Homework 1My Solutions to Homework #1. Note: These vary from well-written to "a little rough".

## Class Notes

Info: These Links are no longer active. Email me if you would like a copy of any of them.

3.1 - Brachistochrone
3.2 - Necessary Conditions
3.3 - Simplest Problem of CoV
3.3 - First Integrals
3.4 - Generalizations
3.5 - Hamilton's Principle
3.6 - Isoperimetric Problems
Lagrange Multiplier Handout

6.1 - Intro to PDEs
6.2 - Conservation Laws in 1D
6.2 - Vector Calc Preliminaries
6.2 - Conservation Laws in 3D
6.2.5 - Boundary Conditions
6.3 - Equilibrium Eqns

4.0 - Prelims to Orthogonality
4.1 - Orthogonality & Fourier Series
4.2 - Sturm Liouville Problems
Updated 4-2-08
6.4.1 - E-vals for the Laplacian
6.4.2 - SoVs Examples
Updated 4-8-08
6.4.2 - More SoVs Examples
(Wave Eqn)
6.5 - Laplace Transforms
6.5 - Fourier Transforms