MATH 6341

MATH 6341 PDE I

Spring 2014

TTr 4:30-6:00 Skiles 133b

Professor Federico Bonetto

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)
- 1.5: 4 (3), 5 (4)
- 2.5: 1

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)
- 2.5: 2, 5 (4)

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)
- 2.5: 6 (5)

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)
- 2.5: 7 (6), 10a (9)

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)
- 2.5: 12 (10), 14 (12)

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)
- 2.5: 15 (13), 17 (14)

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)
- 2.5: 21 (16), 24 (17)

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)
- 3.5: 4, 5, 6

Fifth HW due on Tuesday 11/25.