# Math 647: Theory of Partial Differential Equations 1

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## Contents

## Catalog Information

### Title

Theory of Partial Differential Equations 1.

### Credit Hours

3

### Prerequisite

Math 541, 547. It is proposed that Math 547 be dropped as a prerequisite, as these courses have always operated independently of each other.

### Description

## Desired Learning Outcomes

### Prerequisites

### Minimal learning outcomes

- Foundational theory for canonical linear PDEs
- Transport equation
- Laplace's equation
- Fundamental solution
- Mean-value and maximum principles
- Energy methods

- Heat equation
- Fundamental solution
- Mean-value and maximum principles
- Energy methods

- Wave equation
- Spherical means
- Energy methods

- Method of characteristics
- Sobolev spaces
- Traces
- Sobolev inequalities
- Compactness

### Textbooks

Possible textbooks for this course include (but are not limited to):

- Lawrence C. Evans,
*Partial Differential Equations (Second Edition)*, American Mathematical Society, 2010.

### Additional topics

If time permits, Hamilton-Jacobi equations and/or conservation laws could be introduced.