M 372K, Spring Semester 2010


Partial Differential Equations and Applications


Syllabus


Unique # 57100.

Lectures: Tuesdays and Thursdays, 9:30 - 10:50 AM

Location: RLM 5.124.



Instructor: Thomas Chen
Office: RLM 12.138.
Office hours: Tuesdays and Thursdays, 12 - 1 PM.
Email: t c A_T m a t h . u t e x a s . e d u
Phone: (512) 471 7180


Teaching Assistant: Davi Maximo
Office: RLM 11.114.
Email: m a x i m o A_T m a t h . u t e x a s . e d u


COURSE INFORMATION

Partial differential equations as basic models of flows, diffusion, dispersion, and vibrations. Topics include first- and second-order partial differential equations and classification (particularly the wave, diffusion, and potential equations), and their origins in applications and properties of solutions. Includes the study of characteristics, maximum principles, Green's functions, eigenvalue problems, and Fourier expansion methods. Prerequisite: Mathematics 427K with a grade of at least C.

Links to Blackboard, and to the website of the Registrar.


CLASS MATERIAL

Textbook: Applied Partial Differential Equations with Fourier Series and Boundary Value Problems
Richard Haberman.
4th Edition, Prentice Hall.

Approximate schedule:
Chapter 2 (heat equation, Laplace equation) 2 weeks
Chapter 3 (Fourier series) 1 week
Chapter 4 (wave equation) 1 week
Chapter 5 (Sturm-Liouville theory) 2 weeks
Chapter 6 (numerical methods) 1 week
Chapter 8 (non-homogenous boundary value problems, Poisson equation) 2 weeks
Chapter 9 (Green's functions) 2 weeks
Chapter 10+12 (Fourier transforms, method of characteristics for wave equation) 2 weeks

HOMEWORK

There will be weekly homework assignments posted here. Additional course material will be posted on Blackboard.
Collaborations are encouraged, but you have to present your own solutions. Simply copying somebody else's work is not acceptable.

The handin time of the HW's is at the beginning of the Thursday classes (or earlier).

No late handins are accepted.

HOMEWORK ASSIGNMENTS

  1. HW 1 (due Thursday, January 28, at the beginning of class)
    Exercises 2.2, pg 38 # 1, 2, 3, 4, 5.
    Exercises 2.3, pg 55 # 1, 2-a, 2-d.

  2. HW 2 (due Thursday, February 4, at the beginning of class)
    Exercises 2.3, pg 55 # 6, 7, 11.
    Exercises 2.4, pg 69 # 3, 4.
    Exercises 2.5, pg 85 # 8, 10.

  3. HW 3 (due Thursday, February 11, at the beginning of class)
    Exercises 3.2.1 d, f
    Exercises 3.3.1 e, 3.3.18
    Exercises 3.4.6, 3.4.9, 3.4.12
    Exercise 3.5.1

  4. HW 4 (due on Thursday, February 25, at the beginning of class)
    Exercises 4.4.2 c, 4.4.3, 4.4.7, 4.4.9, 4.4.10, 4.4.11, 4.4.12 (only for the solutions of 4.4.2 c and 4.4.3)

  5. HW 5 (due on Thursday, March 4, at the beginning of class)
    Exercises 5.3.3, 5.3.5, 5.3.8, 5.5.7, 5.5.8-a-b-c, 5.6.2

  6. HW 6 (due on Thursday, March 11, at the beginning of class)
    Exercises 5.10.3, 5.10.6, 6.2.2, 6.3.3, 6.3.9

  7. HW 7 (due on Thursday, March 25, at the beginning of class)
    Reading assignment: Read chapter 6.6 in detail. Exercises: 6.3.12, 6.3.14-1, 6.5.3, 6.6.1-a, 6.6.2-a.

  8. HW 8 (due on Thursday, April 1, at the beginning of class)
    Exercises: 8.2.1-d, 8.2.2-c, 8.3.1-e, 8.3.6, 8.4.1-b, 8.5.1.

  9. HW 9 (due on Thursday, April 15, at the beginning of class)
    Exercises: 8.5.2, 8.5.3, 8.5.4-a, 8.6.1-a, 8.6.2.

  10. HW 10 (due on Thursday, April 22, at the beginning of class)
    Exercises: 9.3.3, 9.3.5, 9.3.6, 9.3.9.

  11. HW 11 (due on Thursday, April 29, at the beginning of class)
    Exercises: 9.4.3, 9.4.5, 10.3.1, 10.3.3, 10.3.8, 10.3.13, 10.3.14.

  12. HW 12 (due on Thursday, May 6, at the beginning of class)
    Exercises: 10.4.4-a, 10.4.5, 10.4.10, 12.3.1.



IN-CLASS EXAMS

There will be 2 in-class exams, during regular class hours, in the usual class room:

EXAM I: Thursday, February 18, 2010.

EXAM II: Tuesday, April 6, 2010.

Please save these dates, there will be no make-up exams !

FINAL EXAM

FINAL EXAM: Thursday, May 13, 9:00 - 12:00 noon. Location: RLM 5.122


It is implicit in your registration for this class that, barring some unforeseen calamity, you affirm to be present to take the final examination at this time.

GRADING

The class grade will be determined as follows:

Homework: 10 percent
Exam 1: 25 percent
Exam 2: 25 percent
Final Exam: 40 percent

Class attendance is required. This is a difficult course that will necessitate a significant investment of time and effort.
If you don't keep track of the material as we go along and stay up to date, you will not be able to catch up later.
The University of Texas at Austin provides upon request appropriate academic accommodations for qualified students with disabilities.
For more information, contact the Office of the Dean of Students at 471-6259, 471-4641 TTY.