MATH 451

Applied Mathematics II
MWF 10-10:50AM in Wilson Hall 1-115

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Info: These Links are no longer active.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
6.1 - Addendum
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

7.1 - Waves and Advection 
7.1 - Advection Eqn and Characteristic Curves
7.2 - Nonlinear Waves
7.1 - Dispersive PDEs

Supplementary Texts:

  1. Applied Partial Differential Equations, J. David Logan
  2. Partial Differential Equations of Mathematical Physics and Integral Eqautions by R.B. Guenther and J.W. Lee
  3. Partial Differential Equations, a Schaum's Outlines text by McGraw Hill

Students are NOT required to buy the supplementary texts. Occasionally, I will cover topics and include material from these texts that are not covered to my satisfaction in the required text.