***This is a course guideline.  Students should contact instructor for the updated information on current course syllabus, textbooks, and course content*

MATH 4335 - Partial Differential Equations I

Prerequisites: MATH 3331, or equivalent, and three additional hours of 3000-4000 level Mathematics. 

Course Description: Initial and boundary value problems, waves and diffusions, reflections, boundary values, Fourier series.

Text: Partial Differential Equations, Second Edition, by Walter Strauss, John Wiley & Sons, Inc. Pub. ISBN: 978-0470054567

Suggested Syllabi:

Chapter 1: Where PDEs come from

1.1 What is a Partial Differential Equation?
1.2 First-Order Linear Equations
1.3 Flows, Vibrations, and Diffusions
1.4 Initial and Boundary Conditions
1.5 Well-Posed Problems

Chapter 2: Waves and Diffusions

2.1 The Wave Equation
2.2 Causality and Energy
2.3 The Diffusion Equation
2.4 Diffusion on the Whole Line
2.5 Comparison of Waves and Diffusions

Chapter 3: Reflections and Sources

3.1 Diffusion on the Half-Line
3.2 Reflections of Waves
3.3 Diffusion with a Source
3.4 Waves with a Source
3.5 Diffusion Revisited

Chapter 4: Boundary Problems

4.1 Separation of Variables, the Dirichlet Condition
4.2 The Neumann Condition
4.3 The Robin Condition

Chapter 5: Fourier Series

5.1 The Coefficients
5.2 Even, Odd, Periodic, and Complex Functions
5.3 Orthogonality and General Fourier Series
5.4 Completeness
5.5 Completeness and the Gibbs Phenomenon

Grading: Please consult your instructor's syllabus regarding any and all grading guidelines.

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