Math 442: Intro to Partial Differential Equations

Fall 2007

Instructor: Andrea K. Barreiro (abarreir (at) math (dot) uiuc (dot) edu)
Office: 337 Illini Hall, (217) 244-2080
Office Hours: T 10:30-11:30, W 2-3
Class Location and Time: MWF 10-10:50 am, 140 Henry Bldg.
Text: Partial Differential Equations: An Introduction, Walter Strauss, 1992.
This website will contain most logistical information for the course. Please check frequently to get homework assignments and announcements.

Announcements

12/10/07

The 2-3 pm office hour I scheduled today conflicts with a previously scheduled commitment. Instead I will be here 3:15-4:15.

12/4/07

The final exam will be December 11, 8-11 am, in our regular classroom. It will be open book and open notes. Here are some more comments and last year's exam.

10/31/07

Last year's exam, and answers. Also try exams on R. Laugesen's website.

10/17/07

Answers to the first exam. The second exam will be in class on November 5. It will cover Chapters 3,4,5.

9/18/07

The exam will cover Chapters 1 and 2. Last semester's exam is here. You can also look at the exams on R. Laugesen's website.

9/17/07

The first exam will be in class on September 26. It is open book and open notes. I will post links to old exams by 9/19.

9/5/07

I will be travelling the week of 9/10-14. Lee DeVille will be lecturing in my place. I have postponed the due date of HW 3 by a week, so that you have 2 homeworks due on 9/21. However please don't procrastinate because they are both quite challenging.

Syllabus

This course will introduce you to partial differential equations (PDEs), which are ubiquitous in physics, biology, and many other fields. We will emphasize the most important PDEs in physics: the wave, diffusion and Laplace equations. Our focus will be on understanding the physical meaning and mathematical properties of their solutions.
The topics we will cover, along with approximately how many class periods we will use to cover them, are:

Chapter 1.1-1.4: Where PDEs come from, and an orientation to some of the basic questions we will be asking about PDEs. (5 lectures)
Chapter 2.1-2.5: Waves and Diffusions (8 lectures)
Chapter 3.3-3.4: Reflections and Sources (3 lectures)
Chapter 4.1-4.2: Boundary problems (3 lectures)
Chapter 5.1-5.6: Fourier series (9 lectures)
Chapter 6.1-6.3: Harmonic Functions (5 lectures)
Chapter 10.1,2,5 Solving the wave, diffusion equations on 2,3D spatial domains. (3 lectures)
Chapter 12.1,3,4: The Fourier Transform and distributions.

Course Requirements

There will be two exams given during the semester, and one final exam. Homework will be assigned every week and must be turned in by 4 pm on the day it is due. The distribution of the final grade will be 20% HW, 40% Exams (20% each) and 40% Final.

Grading and Guidelines for Exams

The approximate dates of the exams are 9/24, 11/5.
Each exam will be curved individually, so that you receive a letter grade (A+ - D-) for each exam in addition to your numerical score.
Alternate times for the in-class exams may be arranged only for a very good reason, and only by prior arrangement. You must take the final at the scheduled time.
Exams will take places during your normal class time. No calculators, cell phones, or ear phones/buds of any kind are permitted.
The final exam will take place at a time determined by the University. The University requires me to give you a failing grade for the course if you fail to take this exam.

Grading and Guidelines for the Homeworks

Homework must be turned in by 4 pm on its due date. Homework can be turned in a) in class, b) at my office (if the door is closed, use the available folder or box), or c) at my mailbox in 250 Altgeld.
Detailed correct solutions with complete explanations are required. Handwriting should be understandable; the grader will not grade a problem if it is unreadable.
For each assignment, I may select a subset of problems that will be graded, so it is to your advantage to do every problem. If you happen to have skipped the problems that are graded that week, you will receive a 0, even if you did all the other problems!
No late homeworks are accepted. However, your two lowest grades will be dropped to allow for illness or emergency situations.
You are encouraged to work together to solve problems; however everyone should turn in their own set of solutions.

Homework Assignments

Homework number	Date due	Problems assigned	Notes
HW 1	8/31/07	1.1 (2abc,3bcef,10,12), 1.2 (1,3,6,7)	1.1 #10: You can quote the result from an ODE textbook
HW 2	9/7/07	1.3 (2,4,6), 1.4 (3,5,6)	1.3 #2: Follow example 2. How this problem differs is that the tension T should be described differently (the tension is the "pull" on the chain); 1.4 #6: This problem is asking you to verify eq. (6), starting from (4),(5) and using irrotationality of v
HW 3	9/21/07	2.1 (1,3,5,8), 2.2 (1,2,3,5)
HW 4	9/21/07	2.3 (1,3,6), 2.4 (4,5,6,9)
HW 5	10/8/07	See PDF
HW 6	10/12/07	4.1 (2,4), 4.2 (2,3)
HW 7	10/26/07	5.1 (1,2,5,8,11), 5.2 (1,4,10)
HW 8	11/09/07	5.3 (7,8), 5.4 (4,8), 5.5 (1,6),5.6 (1,6)	5.5 (6) is hard, I recommend you leave until after the exam. For 5.6 (6), use the harmonic ansatz from the end of Section 5.6
HW 9	11/16/07	6.1 (4,5,10,11), 6.2 (2,3), 6.3 (1,3)
HW 10	12/3/07	10.1 (1,3), 10.2 (1,2,3)

Other Resources

The Mathematics Department Undergraduate Office is generally the place to go for forms, information about a math major/minor, and other questions related to the math program here. The office is located at 313 Altgeld (on the 3rd floor of Altgeld upstairs from the library)

Books on Reserve

The following are on reserve in the Math library (2nd floor of Altgeld Hall):

Boyce and DiPrima, Elementary Differential Equations and Boundary Value Problems: standard ODE textbook, used for Math 441

Brown and Churchill, Fourier Series and Boundary Value Problems: might be a good extra source for Chapter 5

Haberman, Elementary Applied Differential Equations: with Fourier Series and Boundary Value Problems

Additional Tutoring

The Mathematics department offers some free tutoring and maintains a list of tutors for hire.
Tutoring Services

Websites, etc

Mathworld is an online encyclopedia of mathematics which I have found very helpful over the years. You can often get formulas and definitions in an accessible way here.
With the Integrator, you may never have to look at an integral table again.