MATH 4335 - Partial Differential Equations I & Math 4336 - Partial Differential Equations II - University of Houston

# MATH 4335 - Partial Differential Equations I & Math 4336 - Partial Differential Equations II

***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

Math 4336 - Partial Differential Equations II

Prerequisites: MATH 4335 and MATH 3331

Course Description: Existence and uniqueness for Cauchy and Dirichlet problems; classification of equations; potential-theoretic methods; other topics at the discretion of the instructor.

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

Suggested Syllabus

Chapter 6: Harmonic Functions

6.1 Laplace's Equation
6.2 Rectangles and Cubes
6.3 Poisson's Formula

Chapter 7: Green's Identities and Green's Functions

7.1 Green's First Identity
7.2 Green's Second Identity
7.3 Green's Functions
7.4 Half-Space and Sphere

Chapter 9: Waves in Space

9.1 Energy and Causality
9.2 The Wave Equation in Space-Time
9.3 Rays, Singularities, and Sources

Chapter 10: Boundaries in the Plane and in Space

10.1 Fourier's Method, Revisited
10.3 Solid Vibrations in a Ball

Chapter 11: General Eigenvalue Problems

11.1 The Eigenvalues Are Minima of the Potential Energy
11.2 Computation of Eigenvalues
11.3 Completeness
11.4 Symmetric Differential Operators
11.5 Completeness and Separation of Variables
11.6 Asymptotics of the Eigenvalues

Syllabus by David Wagner