Applied Mathematics (4rth ed)    -  J. David Logan

•   Chapter 1 Dimensional Analysis and Scaling
•   Chapter 3 Perturbation Methods
•   Chapter 4 Calculus of Variations

MWF 10-10:50 , Wil 1-143

Grades will be recorded in D2L. The course % will determined as follows:

HOMEWORK:

NOTES 

Conversion to letter grade:

Homework and due dates will be posted here as class develops. Homework assignments will have varied lengths and difficulty hence will have different raw scores. The HW% for the final grade will be the % from the sum of all the raw HW scores:

Periodically I will post handwritten and/or typeset lecture notes here.

M450 Notes:

1. Dimensional Analysis (Text Chapter 1)

1. Dimensional Analysis Introductory examples. and Similarity Solns.
2. Dimensional Analysis Theory
3. Scaling in differential equations (nondimensionalization)

2. Perturbation Theory (Chapter 3)

1. Introductory Problems
2. Regular Perturbation Problems - algebraic
3. Regular Perturbation Problems - Systems and Integrals
4. Regular Perturbation Problems - ordinary differential equation
5. Regular Perturbation Problems - nonlinear oscillations
6. Asymptotics
7. Singular Perturbation Theory - algebraic 
8. Singular Perturbation Theory - BVP intro
9. Singular Perturbation Theory - BVP Matching
10. Singular Perturbation Theory - BVP worked examples
11. Singular Perturbation Theory - BVP Matching failure
12. Singular Perturbation Theory - IVP Oscillator example, Chemical Model example

3. Calculus of Variations (Chapter 4)

1. Calculus of Variations - Introduction
2. Calculus of Variation - Theory 
3. Euler-Lagrange equations - Necessary conditions for minima
4. Natural Boundary Conditions
5. Principle of Least Action
6. Higher Dimensional Problems
   1. Spring-Pendulum example
   2. Geodesics
7. Isoperimetric Constraints - example

M451 Notes:

1. Function Expansions

1. Generalized Fourier Series
2. Sturm Liouville Theory

2. Green's Functions

1. Introduction to Green's Functions
2. Fredholm Integral Equations (no HW on this)
3. Distributions introduction

3. Partial Differential Equations

1. Introduction and Examples
2. Series Solutions
3. Conservation Laws
4. Multivariate Calculus Review
5. Diffusion and Random Walks
6. Method of Characteristics