Math 442
Intro to Partial Differential Equations (PDEs)
Spring 2022



Syllabus

This course introduces students to partial differential equations, emphasizing the wave, diffusion and Laplace equations. The focus is on understanding the physical meaning and mathematical properties of solutions of partial differential equations. Methods include fundamental solutions and transform methods for problems on the line, and separation of variables using orthogonal series for problems in regions with boundary. Convergence of Fourier series is covered in detail.


Professor:Kay Kirkpatrick
Contact:kkirkpat(at)illinois.edu (please put "442" in the subject) or through Canvas
Websites:https://math.uiuc.edu/~kkirkpat/442sp2022.html (limited) and Canvas (more complete). Department syllabus: https://math.illinois.edu/resources/department-resources/syllabus-math-442
Time and place: Section E13/14: 1:00PM - 1:50PM on MWF in Zoom (see Canvas for link)
Section G13/14: 3:00PM - 3:50PM on MWF in Zoom (see Canvas for link)
Student hours: Mondays and Fridays at 4pm on Zoom, or by appointment. I would be happy to answer your questions anytime as long as I'm not otherwise engaged, and before and after class are also good times to catch me.
Prerequisite: One of MATH 284, MATH 285, MATH 286, or MATH 441.
Textbook: Walter A. Strauss, Partial Differential Equations: An Introduction, John Wiley & Sons, 2008 (2nd ed.). Other editions are okay for studying; homework problems come from the official edition. There may be an online copy available.
Homework policy: Homework will be assigned regularly and collected online in Canvas. You are encouraged to work together on the homework, but you should write up your own solutions to turn in separately. Late homework will not be accepted or graded; instead I will drop your three lowest homework scores.
Homework philosophy: Mathematics is something that we learn by doing: doing homework problems and explaining them to each other. If, after thinking about them, you get stuck or have questions, I will be happy to help. You'll have a high probability of doing well in this class by combining all of these resources: classes, textbook, homework, office hours, and discussions with classmates.
Exams: We will have 3 midterms, and they are scheduled to be independent of our class meeting time, on Feb 11, Mar 11, and Apr 22. All exams will be open-book, open-notes, and take-at-home. The exam will be provided as a PDF file on Canvas, and then you will upload your answers into Canvas. Ideally, you will have online access, printer/scanner access or tablet-mark-up access, in order to take the exams. Please let me know ASAP if you don't have access to something. Each exam will be technically comprehensive but emphasizing recent material up to the most recent graded and returned homework assignment. The final exam will cover important topics of the whole course, emphasizing recent material somewhat. The final exam is open-book, open-notes, take-at-home, and on this schedule:

Section E13/14: 8:00-11:00 a.m., Friday, May 13
Section G13/14: 7:00-10:00 p.m., Tuesday, May 10
Exam policy: Make-up exams will be given only for medical or other serious reasons, and arrangements should be initiated by you as soon as possible. You must work completely on your own during exams and quizzes. My exams are fair and similar to homework, so as long as you use the resources provided, you should be fine. If you have difficulties or fall behind in the course, please come talk to me.
Grading policy: Homework: 20% of the course grade
3 Midterms: 20% each
Final Exam: 20%
There will probably be a curve for the semester letter grades; 90% would be the highest cutoff for an A-, 80% for a B-, and so on. If you are near a cutoff, I take your attendance and lecture participation into account.
Justice: I am committed to affirming the identities, realities and voices of all students, especially students from historically marginalized or under-represented backgrounds. I value the use of self-specified gender pronouns and respect for all persons. Please contact me to receive disability accommodations. You should also know that I'm a mandatory reporter.

Homework assignments and lecture notess (to be updated in Canvas)


Week 1: Introduction: sections 1.1, 1.2
Wednesday lecture notes
Friday lecture slides

HW #1, due by 5pm the first Friday: please send me an email introducing yourself, for instance, what name you prefer to be called, your major and hobbies, why you're interested in PDEs, or anything else you want to share or have questions about. If you want to to attach a photo of yourself (other than your Zoom profile) to help me connect your face with your name, that would be great (but is not required).

Week 2: sections 1.3, 1.4, 1.5
Monday: lecture
Wednesday: lecture
Friday: lecture

HW #2, due by the end of class on the second Friday of the semester: Section 1.1: 11, 12; Section 1.2: 2, 7, 8.


Emergency information links.