# Math 647: Theory of Partial Differential Equations 1

From MathWiki

## 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

### Textbooks

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

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