### MATH 6341 PDE I

### Spring 2014

### TTr 4:30-6:00 Skiles 133b

### Office Hours: TTr 6:00-7:00 in Skiles 224

If you have problem to meet me during the scheduled time, email me to
set an appointment.

Syllabus
See online syllabus at MATH
6321.

We will concentrate on Part I of the text book. We will cover
Chapter 2 and 3 and selected arguments from Chapter 4.

#### Prerequisite

MATH 4318

#### Textbook

Lawrence C. Evans "Partial Differential Equation", AMS

#### Grading

I will collect HW every 2 weeks for a total of 5/6 HW. On top there
will be two in class midterms and a in class final. Midterms and final
will be cumulative. The possibility of personal project will be
discussed later during the class. The grading scheme will be 15% HW,
35% midterms and 50% final.

**First week**

- Material covered
- 1. Inroduction

- 2.1 Transport Equation
- 2.2.1 Laplaces's Equation: Doundamental Solution

- Exercises (numbers in parentheses are for the 1st edition)

**Second week**
- Material covered
- 2.2.2 Mean Value Formula

- 2.2.3 Properties of Harmonic Functions

- Exercises (numbers in parentheses are for the 1st edition)

First HW due on Thursday 9/4. Solution set for HW 1.

**Third week**
- Material covered

- 2.2.3 Properties of Harmonic Functions (continued)

- Exercises (numbers in parentheses are for the 1st edition)

**Fourth week**
- Material covered

- 2.2.3 Properties of Harmonic Functions (continued)
- 2.2.4 Green's Function

- Exercises (numbers in parentheses are for the 1st edition)

Second HW due on Tuesday 9/23. Solution set for
HW 2.

Fifth week
- Material covered

- 2.2.5 Energy Methods
- 2.3.1 Heat Equation: Fundamental Solution

- Exercises (numbers in parentheses are for the 1st edition)

**Sixth week**
- Material covered

- 2.3.2 Mean Value Formula
- 2.3.3 Properties of Solutions

- Exercises (numbers in parentheses are for the 1st edition)

First Midterm will be Tuesday 10/28. Solution set for the first midterm.

**Seventh week**
- Material covered

- 2.3.3 Properties of Solutions (continued)
- 2.3.4 Energy Methods

Third HW due on Tuesday 10/7. Solution set for
HW 3.

**Eighth week**
- Material covered

- 2.4.1 Wave Equation: Solution by Spherical Means.(n=1,2,3
only)

**Nineth week**
- Material covered

- 2.4.2 Nonhomogeneous Problem.
- 2.4.3 Energy Methods

- Exercises (numbers in parentheses are for the 1st edition)

Fourth HW due on Tuesday 10/30.

**Tenth week**
- Material covered

- 3.2.1 Characteristic: Derivation of Characteristic ODE
- 3.2.2 Examples

Eleventh week
- Material covered

- 3.2.3 Boundary Condition (Sketched)

- 3.2.4 Local Solution

- Exercises (numbers in parentheses are for the 1st edition)

Fifth HW due on Tuesday 11/25.