# 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. 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

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.

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 12, 8:00am—10:00am in the classroom, BLOC 160