# Difference between revisions of "Math 647: Theory of Partial Differential Equations 1"

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#* Transport equation | #* Transport equation | ||

#* Laplace's equation | #* Laplace's equation | ||

+ | #** Fundamental solution | ||

+ | #** Mean-value and maximum principles | ||

+ | #** Energy methods | ||

#* Heat equation | #* Heat equation | ||

+ | #** Fundamental solution | ||

+ | #** Mean-value and maximum principles | ||

+ | #** Energy methods | ||

#* Wave equation | #* Wave equation | ||

+ | #** Spherical means | ||

+ | #** Energy methods | ||

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## Revision as of 11:52, 31 May 2011

## 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.