Math 602 - Fall 2016

Instructor: Bojan Popov                                          
Office: Blocker 507B                                                   
Email:  popov"at"math.tamu.edu                                                                                     
Office Hours: TR 10:25-11:25, or by appointment
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, and 10.4 only); Chapter 9 (Green's functions... until we run out of time)


Homework assignments:

Lecture 1: Tuesday, August 30. We covered 1.1 and 1.2.
Lecture 2. Thursday, September 1. We covered sections 1.3, 1.4. and 1.5 and solved problems from/similar to the first homework.
Lecture 3. Tuesday, September 6. We covered sections 2.1, 2.2 and 2.3.
Lecture 4. Thursday, September 8. Quiz 1 (15 min in the beginning of class based on Chapter 1). We covered sections 2.3 and some of 2.4.
Lecture 5. Tuesday, September 13. We covered sections 2.4 and a part of 2.5 - Laplace's equation in 2D for a rectangle.
Lecture 6. Thursday, September 15. We covered the rest of Chapter 2.
Lecture 7. Tuesday, September 20. We covered sections 3.1 and 3.2 and started 3.3
Lecture 8. Thursday, September 22. Quiz 2 (15 min in the beginning of class based on Chapter 2). We covered sections 3.3 and 3.4.
Lecture 9. Tuesday, September 27. We covered section 3.5.
Lecture 10. Thursday, September 29. Problems solving session from HW3 and suggested HW4 - on Fourier series. Solutions for  Quiz 1  Quiz 2
Lecture 11. Tuesday,  October 4. EXAM I  -- five problems from Chapters 1,2,3.
Lecture 12. Thursday, October 6. Chapter 4 - Linear wave equation in 1D: Sections 4.1 and 4.2.
Lecture 13. Tuesday,  October 11. Sections 4.3 and 4.4.
Lecture 14. Thursday, October 13. Sections 4.5, 12.1 and 12.2.
Lecture 15. Tuesday,  October 18. Sections 12.2 and problem solving.
Lecture 16. Thursday, October 20. Quiz 3 (15 min in the beginning of class based on Chapter 4). Section 12.3. and 12.4.  Quiz 3
Lecture 17. Tuesday,  October 25. Section 12.4 and 12.5; methods of extensions and characteristics, problem solving session.
Lecture 18. Thursday, October 27. Section 12.6 and 12.2-3 revisited. Nonlinear hyperbolic models.
Lecture 19. Tuesday,  November 1. Shocks and expansion waves, problem solving session from 12.6.
Lecture 20. Thursday, November 3. Weak solutions, Rankine-Hugoniot condition, nonuniqueness of discontinuous solutions.
Lecture 21: Tuesday,  November 8.  Section 12.6: Shocks and rarefactions, examples; Non uniqueness of discontinuous solutions; entropy solutions, viscosity limits
Lecture 22: Thursday, November  10 Review for the second exam: Chapter 4 and Chapter 12
Lecture 23: Tuesday,  November 15. EXAM II (in class)
Lecture 24: Thursday, November 17. Section 10.1-3
Lecture 25: Tuesday,  November 22. Section 10.4, sourse and reaction terms, influence functions and using delta measures or Fourier approach to compute them.
Lecture 26: Tuesday,  November 28. Duhamel's principle and sections 9.1- 9.2
Lecture 27: Thursday, December 1. Section 9.3 and computations of Green's functions
Lecture 28: Tuesday,  December 3.
General review:
    1. Heat equation,
    2. Laplace's
    3. Fourier series.
    4. Linear wave equation (via Fourier or characteristics);
    5. Transport equation;
    6. Nonlinear conservation laws (expansions; shocks, interactions);
    7. Fourier transform (10.4); Green's function (9.3) - look at the solution keys for Chapters 9&10 and problem #7 from the Old final
Exam solutions:  Exam1page1    Exam1page2    Exam1page3    Exam1page4    Exam1page5 -- Exam2page1    Exam2page2    Exam2page3    Exam2page4   
Final exam:  December  14, 2015;    1:00-3:00 p.m.