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Department:

MATH

Course Number:

6341

Hours - Lecture:

3

Hours - Lab:

0

Hours - Recitation:

0

Hours - Total Credit:

3

Typical Scheduling:

Every fall semester

Introduction to the mathematical theory of partial differential equations covering the basic linear models of science and exact solution techniques.

Prerequisites:

Course Text:

No text

Topic Outline:

- Derivation of Basic Models
- Constitutive relations, conservation principles
- Wave, diffusion, and potential equations
- Initial and boundary value problems
- Existence and uniqueness

- Types of Equations
- Classification of first and second order equations
- Laplace and Poisson equations
- maximum principles
- mean value properties
- regularity

- Heat equation
- maximum principles
- regularity

- Transport and wave equations
- characteristics
- Huyghen's principle

- Miscellaneous equations
- Schrödinger's equation
- conservation laws
- reaction-diffusion equations

- Methods of Exact Solution
- Fourier series
- Fourier transform
- Fundamental solutions and Green's functions
- Method of characteristics
- Kirchoff's formula and the method of descent
- Power series, Cauchy-Kowalevski and Holmgren theorems

- Distributions
- Miscellaneous Topics
- Asymptotic expansion
- Energy methods