**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. Short
solution

**Lecture 2. **Friday, August
26, 2022. We covered sections 1.5 and 1.3 and
solved
a few problems in class.

**Lecture 3.** Monday, August
29, 2022. We covered sections 14., 2.1 and 2.2.

**Lecture 4. **Wednesday,
August 31, 2022. We covered sections 2.2 again, 2.3 and 2.4.

Homework
2: due
**September
16**:
**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.
HW2
solution

**Lecture 5. **Friday,
September 2. We covered 2.3 and 2.4 again and solved examples.

**Lecture 6.**
Wednesday, September 7. Section 2.3 and 2.4.
Practice problems.

**Lecture 7. **Friday,
September 9. Section 2.5.1. Homework 1 was due.

**Lecture 8.**
Monday,
September 12. Section 2.5.2. and some more problems
from of 2.5.1. Try to solve problems like 2.5.1 and 2.5.5 on pages
81-82.

**Lecture 9.**
Wednesday, September 14. More from Section 2.5. Here is a
sample test

**Lecture
10. **Friday,
September 16. Homework 2 is due. We covered Sections 3.1.and 3.2

Here are a few more sample questions for the exam: old quiz and another old one

and a link to my old notes on Laplace equation … Laplace

**Lecture
11.** Monday,
September 19. Review for Exam 1. The exam will be either four or five
problems. Review the sample exams, quizzes, HW1&2.

Review 412: Questions 1 and 2 from the quizzes; Sample test:
#1,2,3 and #6; Section 1.4 type questions

Summary: Laplace with
one non-zero BC, polar, total heat energy, equilibrium, heat
equation, energy method

**Lecture 12.**
Wednesday, September 21. EXAM I.

**Lecture
13. **Friday,
September 23. We covered Sections 3.2 and 3.3
again.

**Lecture
14.** Monday,
September 26. Section 3.4 = differentiation of Fourier series.

Homework
3 due Monday,
October 3: 3.2.1
(a,c), **3.2.4, 3.3.4,
3.4.1, 3.4.2, 3.4.3 solution-page
1, solution-page
2, solution-page**

**Lecture 15.** Wednesday, September 28. We covered 3.4
again and 3.5. Work on the homework!

**Lecture 16.**
Friday, September 30. Sections 3.5 and 3.6. Review of Chapter 3.

**Lecture 17.** Monday, October 3. We
covered Sections 4.1, 4.2 and 4.4.

**Lecture 18.** Wednesday, October 5. Return of Exam 1. We
covered sections 4.3, and 4.4 again.

Homework
4 due October
14: **4.4.8, 4.4.9,
4.4.10, 4.4.11, 4.4.12; **__Homework
4 solutions__

**Lecture 19.** Wednesday, October 7. We
covered 12.1-12.2.

Homework
5 due October
21: **12.2.3, 12.2.4,
12.2.7, 12.4.1, 12.4.2 **__Homework
5 solutions__

**Lecture 20.**
Wednesday, October 12. Worked on HW4 and covered Section 12.2.

**Lecture 21.**
Friday, October 14. Section 12.2
again...

**Lecture 22.** Monday, October 17. Sections 12.3 and 12.4.

**Lecture 23.**
Wednesday, October 19. Chapter 12.1-4 review.

**Lecture 24.** Friday, October
21. Review for Exam 2.

For
Fourier series: solve 4 and 5 from this sample
test 1

For Chapter 4 wave equation questions solve problems
1 and 2 from the sample
midterm 2

For the method of characteristics solve problems
3, 4, 5(i) from the sample
midterm 2

For section 12.4 solve problems 12.4.1 and
12.4.2

Here is my hand written solution of the sample midterms
2: page1,
page2,
page3,
page4,
page5,
page6

The
exam will have: one Fourier series; one wave equation; one linear
transport; one nonlinear transport; and maybe one more.**
Lecture
25.** Monday, October 24. EXAM
II - in class, 4 or 5 problems.

**Lecture 26.** Wednesday, October
26. Discontinuous data: Expansion waves.
Notes

**Lecture 27.**
Friday, October 28. Discontinuous data:
Shock waves. Notes

**Homework
6 ****due
Monday, November 7: 12.2.5 (b,c), 12.2.8, 12.3.5, 12.6.7 Homework
6 solution**

**Lecture 28.** Monday, October 31. More
shock waves, Rankine-Hugoniot condition -- equation (12.6.22),
examples and problem solving. Notes

**Lecture 29.** Wednesday,
November 2, problem solving session from chapter 12

**Lecture 30.** Friday, November
4, end of Chapter 12, Notes

Extra -- bonus HW problems from Chapter 12, due December 2

**Lecture 31.** Monday, November 7. Sections
10.1 and 10.2. Fourier transform motivation via Heat equation on
infinite domain.

Homework 7 due November 18 (at the beginning of class): 10.3.6, 10.3.7, 10.4.3, 10.4.4

Homework 7 solutions 10.3 Homework 7 solutions 10.4

**Lecture 32. **Wednesday,
November 9, Sections 10.3 +
Fourier series (complex form) + influence function derivation 10.4.1

**Lecture 33. **Friday,
November 11. Dirac delta measure
and
the heat equation. Section 10.3 and
10.4.

**Lecture 34.** Monday, November
14. Section 10.4.3. Convolution theorem, general heat equation.

**Lecture 35. **Wednesday,
November 16. General Heat equation, here are the notes: page1,
page2,
page3

Heat equation with a source term. Duhamel's principle.

**Lecture 36. **Friday,
November 18. **Exam 2 – returned and solved in class **

**Lecture 37.** Monday, November
21. Sections 9.1 and 9.2.

**Lecture 38.** Monday, November
28. Section 9.3. Homework
8 **NOT
due** 9.3.5
a,b,c, 9.3.6
a, 9.3.11,
9.3.21 Homework
8 p.1 Homework 8 p.2 Homework
8 p.2

**Lecture 39. **Wednesday,
November 30. Section 9.3 again. Finding the Greens function via Dirac
delta.

Here are the notes for Chapter 9: November 28, November 30

**Lecture 40.** Friday, December 2. Review of Chapters 9 and
10.

**Lecture 41.** Monday, December 5. Review of Chapter 12.

Solution of Exam 1 Solution of Exam 2

**Lecture 42.** Wednesday, December 6. General review. here is
a sample
test and three more
problems here (#1,2,3 only) and and
more practice questions

**Final
Exam, December 1****2****,
8:00am—10:00am in the classroom, BLOC 160 **