Math 412 - Fall 2020

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)
Midterm I: September 10, 2020; Midterm II: October 15, 2020; Final Exam: December 2, 2020

Lecture 1. Thursday, August 20, 2020: We covered sections 1.1, 1.2, and 1.5. Read 1.3-1.4 and work on the homework.
Homework 1: HW1, (short solution): 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 Tuesday Sept 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; submit only the bold problems

Lecture 2. Tuesday, August 25, We covered sections 1.5, 1.3, 1.4.

Lecture 3. Thursday, August 27, We covered sections 2.1, 2.2, and part of 2.3.

Lecture 4. Tuesday, September 1. We covered 2.3 including section 2.3.6. again and section 2.4

Lecture 5. Thursday, September 3. We covered section 2.4 again covered section 2.5

Homework 2: due Tuesday Sept. 8: 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 6. Tuesday, September 8. Review for Exam 1: sections 1.3, 1.4, 1.5 and 2.1, 2.2, 2.3, 2.4 and 2.5 Laplace's equation on a disk

Lecture 7. Thursday, September 10, 2020. EXAM I - during class time on zoom and ecamus
Lecture 8. Tuesday, September 15. We covered 3.1 and 3.2 .
Homework 3 due Monday Sept 28: 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 9. Thursday, September 17. We covered 3.3 and a part of 3.4. I discussed the first exam.
Lecture 10. Tuesday, September 22. We covered section 3.4. Review of Chapter 3.
Lecture 11. Thursday, September 24. We covered 4.1, 4.2, and 4.4.
Lecture 12. Tuesday, September 29, 2020. We covered sections 4.3 and 4.4, and 12.1.
    Homework 4 due October 12: 4.4.8, 4.4.9, 4.4.10, 4.4.11, 4.4.12 Homework 4 solutions
Lecture 13. Thursday, October 1. We covered 12.2. - problem solving session for transport problems.
Lecture 14. Tuesday October 6. We covered 12.3 + uniqueness via energy arguments; 12.4
   Homework 5 due October 14: 12.2.3, 12.2.4, 12.2.7, 12.4.1, 12.4.2   Homework 5 solutions
Lecture 15. Thursday, October 8. Sections 12.4 and 12.5 - geveral review of method of characteristics for the wave equation.
Lecture 16. Tuesday October 13. Review for Exam 2. Fourier series, 1d wave equation with Fourier, 1d wave with method of characteristics, transport equation.
For Fourier series: solve 4 and 5 from this sample test 1
For Chaper 4 wave equation questions solve problems 1 and 2 from the sample midterm 2
For the method of chanracteristics 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 writen solution of the sample midterms 2: page1, page2, page3, page4, page5, page6
Lecture 17. Thursday October 15. EXAM 2 - during class time on zoom and ecamus
Lecture 18. Tuesday October 20. Section 12.6.1-4. Method of characteristics again, nonlinear case. Shock waves.
    Homework 6 due Friday Oct 30: 12.2.5 (b,c), 12.2.8, 12.3.5, 12.6.7   Homework 6 solution
Lecture 19. Thursday October 22. More shock waves, examples, Rankine-Hugoniot condition -- equation (12.6.22
Lecture 20. Tuesday October 27. Return and review of Exam 2. Last lecture on Conservation Laws: general waves, equal area rule. Bonus HW posted.
         Extra/bonus HW problems from Chapter 12, due December 1
Lecture 21. Thursday October 29. Sections 10.1 and 10.2. Fourier transform motivation via Heat equation on infinite domain.
    Homework 7 due November 17 (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 22. Tuesday, November 3. Sections 10.3 + Fourier series (complex form) + influence function derivation 10.4.1
Lecture 23. Thursday, November 5. Sections 10.4.1 again, 10.4.2 and 10.4.3.

Lecture 24. Tuesday, November 10. Heat equation with a source term. Proof of Duhamel's principle
Lecture 25. Thursday, November 12. General Heat equation, here are the notes: page1, page2, page3
and Section 9.1 and 9.2.

Lecture 26. Tuesday, November 17. Section 9.3.
Lecture 27. Thursday, November 19.
Lecture 28. Tuesday, November 24. General review, here is a sample test

Office hour on December 1 at 3:15pm - on our regular zoom link

Final exam date: December 2, 2020, 2:00 p.m.-4:30 p.m. on ZOOM