# Math 412 - Fall 2022

**Course Information**: First
day handout

**Outline: **Chapter
1 (heat equation); Chapter 2 (including max. principle - section 2.5.4);
Chapter 3 (will not cover 3.6); Chapter 4 (4.1,4.2,4.3, and 4.4. only); Chapter
12 (including 12.6); Chapter 10 (10.1, 10.2, 10.3, 10.4 only); Chapter 9
(Green's functions until we run out of time)

**Lecture 1. **Wednesday,
August 24, 2022. We covered sections 1.1. and 1.2. Read 1.3 and 1.4 and
start the homework.

Homework 1: **1.3.1**, 1.4.1(b) (g), **1.4.3**, 1.4.10, 1.5.5, **1.5.8**,
1.5.11, 1.5.14 due **September
9 in class** submit only the bold problems.

**Old schedule … here:**

**Lecture 1.** Monday, August 30**.** We
covered sections 1.1, 1.2, and 1.5. Read 1.3-1.4 and work on the homework.

Homework 1: **1.3.1**, 1.4.1(b) (g), **1.4.3**, 1.4.10,
1.5.5, **1.5.8**, 1.5.11, 1.5.14 due **September 10 in class** submit only the bold problems.

**Lecture 2.** Wednesday, September 1. We covered sections 1.5, 1.3, 1.4.

Lecture 3. Friday, September 3, We covered sections 2.1 and 2.2.

Lecture 4. Monday, September 6, We covered covered 2.3 including section
2.3.6. Continue from 2.3.7 next time.

**Lecture 5.** Wednesday, September 8. We covered 2.3.7 and 2.4. Here is

Homework 2: due **Friday**
**Sept. 17**: **2.2.2,** 2.3.2 (a) (c), **2.3.3 (a)**
(b), **2.3.5, 2.4.3, 2.4.4,**
2.4.6

**Lecture 6.** Friday, September 10. Section 2.4.2 again and Section 2.5.1 .
Try problems like 2.5.1 and 2.5.5 on pages 81-82.

**Lecture 7.** Monday, September 13, We covered Sections 2.4.2 again

**Lecture 8.** Wednesday, September 15. We covered section 2.5.2.

**Lecture 9.** Friday, September 17. Review for Exam 1. Here are a few
sample questions: and another

**Lecture 10.** Monday, September 20. EXAM I - in
class

**Lecture 11.** Wednesday, September 22. We covered 3.1, 3.2 and 3.3.

Homework 3 due Friday, October 1: 3.2.1 (a,c), **3.2.4, 3.3.4, 3.4.1, 3.4.2, 3.4.3 **

**Lecture 12.** Friday, September 24. We covered 3.4. and solved some
problems similar to the homework.

Lecture 13. Monday, September 27. We covered 3.5. Return of Exam 1. Review
of Chapter 3.

**Lecture 14.** Wednesday, September 29. We covered 4.1, 4.2 and 4.4.

**Lecture 15.** Friday, October 1. We covered sections 4.3, and 4.4 again.

Homework 4 due October 11: **4.4.8, 4.4.9,
4.4.10, 4.4.11, 4.4.12;**

**Lecture 16.** Monday, October 4. We covered 12.1-12.2.

**Lecture 17.** Wednesday, October 6. We covered Chapter 4 again and 12.3.

**Lecture 18.** Friday, October 8. Sections 12.2 and 12.4.

Homework 5 due October 18: **12.2.3, 12.2.4,
12.2.7, 12.4.1, 12.4.2**

**Lecture 19.** Monday, October 11. Section 12.4.

**Lecture 20.** Wednesday, October 13. Section 12.5.

**Lecture 21.** Friday, October 15. Chapter 12 - method of characteristics,
problem solving session.

**Lecture 22.** Monday, October 18. Review for Exam 2

For Fourier series: solve
4 and 5 from this

For Chaper 4 wave equation questions solve problems 1 and 2 from the

For the method of characteristics solve problems 3, 4, 5(i) from the

For section 12.4 solve problems 12.4.1 and 12.4.2

Here is my solution of the sample midterms 2:

The exam will have: one Fouries series; one wave equation; one linear
transport; one nonlinear transport; and maybe one more.

Lecture 23. Wednesday, October 20. EXAM II - in
class, 4 or 5 problems.

Homework 6 due Wednesday, November 3: **12.2.5
(b,c), 12.2.8, 12.3.5, 12.6.7**

**Lecture 24.** Friday, October 22. Shock waves: Rankine-Hugoniot condition -- equation (12.6.22)

Extra -- bonus HW problems from
Chapter 12, due December 1

**Lecture 25.** Monday, October 25. More shock waves, examples...

Office hours are in person now in: Bloc 507B (MW 12:50-1:40)

**Lecture 26.** Wednesday, October 27. General waves, equal area
rule, wave interactions.

**Lecture 27.** Friday, October 29. Wave interactions.

**Lecture 28.** Monday, November 1. Chapter 12 review, bonus problems
discussion.

Homework 7 due November 22 (at the beginning of class): 10.3.6, 10.3.7, 10.4.3, 10.4.4

**Lecture 29.** Wednesday, November 3. Sections 10.1 and 10.2. Fourier transform motivation via Heat
equation on infinite domain.

**Lecture 30.** Friday, November 5. EXAM II -
returned and solved in class.

**Lecture 31.** Monday, November 8. Sections 10.3 + Fourier series (complex
form) + influence function derivation 10.4.1

**Lecture 32.** Wednesday, November 10. Sections 10.4.1 again, 10.4.2 and
10.4.3.

**Lecture 33.** Friday, November 12. Dirac delta measure as initial
condition for the heat equation.

**Lecture 34.** Monday, November 15. General Heat equation, here are the
notes:

**Lecture 35.** Wednesday, November 17. Heat equation with a source term.
Duhamel's principle

**Lecture 36.** Friday, November 19. Section 9.1 and 9.2.

Homework 8 due December 6, 9.3.5 a,b,c, 9.3.6 a, 9.3.11, 9.3.21

**Lecture 37.** Monday, November 22. Section 9.3

**Lecture 38.** Monday, November 29. Problem solving from Chapter 9.

**Lecture 39.** Wednesday, December 1. Review of Chapters 9

**Lecture 40.** Friday, December 3. Review of Chapters 10 and 12.

**Lecture 41.** Monday, December 6. General review. here is a sample
test and three more problems here
(#1,2,3 only) and and more practice
questions