Math 442
Intro to Partial Differential Equations (PDEs)
Spring 2020


Announcement in light of COVID-19:



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Course webpage: https://faculty.math.illinois.edu/~kkirkpat/442spring2020.html.
Department syllabus: https://math.illinois.edu/resources/department-resources/syllabus-math-442


Professor:Kay Kirkpatrick
Contact:The way to get in touch with me is by email, kkirkpat(at)illinois.edu, with "Math 442" in the subject line and addressing me as "Professor Kirkpatrick." If you're expecting an email from me and haven't received it, please check all of your spam filters.
Time and place: Section X13/14: 12:00PM - 12:50PM on MWF in 156 Henry Administration Building
Office hours: Mondays 4:00-4:50 pm, and Fridays 11:00-11:50am, or by appointment, in my office, 231 Illini Hall. I would be happy to answer your questions in my office anytime as long as I'm not otherwise engaged. You are also welcome to ask questions before, during, and after class.
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.
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 in class. You may turn HW in to my mailbox in 250 AH before the end of class; homework turned in at my office will not be accepted. You are encouraged to work together on the homework, but you should write up your own solutions to turn in separately. If you go by two names, please put both of them on your homework. Late homework will not be accepted or graded; instead I will drop your two lowest scores.
Homework philosophy: Mathematics is something that you 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: Two in-class midterms are scheduled for February 21 and April 3. 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 8:00-11:00 a.m., Friday, May 15.
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
2 Midterms: 20% each
Final Exam: 40%
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.
Prerequisites: One of MATH 284, MATH 285, MATH 286, MATH 441.

Homework assignments and lectures (to be updated)



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

HW #0, due by 5pm the first Friday of the semester: 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. It would also be helpful to attach a photo of yourself to help me connect your face with your name.

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

HW #1, due by the end of class on the second Friday of the semester (Jan. 31): Section 1.1: 11, 12; Section 1.2: 2, 7, 8.

Week 3: sections 2.1, 2.2
Monday: lecture
Wednesday: lecture
Friday: lecture

HW #2, due by the end of class on the third Friday of the semester (Feb. 7): Section 1.3. #4; Section 1.4. #5; Section 1.5. #1, #2, #5

Week 4: sections 2.2, 2.3, 2.4
Monday: lecture
Wednesday: lecture
Friday: lecture

ANNOUNCEMENT: there will be a quiz in class on February 14, one week before the first midterm. The quiz will cover HWs that have been graded and returned beforehand. If you do well on the quiz, it will replace one of your low HW scores; if not, I'll drop the quiz.

HW #3, due by the end of class on the 4th Friday of the semester (Feb. 14): Section 2.1. #1, #3, #5; Section 2.2. #1, #2

Week 5: sections 2.4, 2.5
Monday: lecture
Wednesday: lecture
Friday: Midterm 1. Sample Midterm 1 from another professor. My midterm will be different. Please study your HW problems and the lecture material. Resources from Saundra Yancy McGuire and Stephanie McGuire's books on metacognition: Appendices A and B. If you'd like to know more, I recommend getting a copy of Teach Yourself How to Learn or watching a talk by Saundra McGuire or looking at my copy in my office.



Week 6: sections 2.5, 3.1, 3.3, 3.4
Monday: lecture
Wednesday: lecture
Friday: lecture

HW #4, due by the end of class on the 6th Friday of the semester (Feb. 28): Section 2.3. #4, #5; Section 2.4. #3, #9-10, #16



Week 7: sections 3.4, 4.1, 4.2, 4.3
Monday: lecture cancelled
Wednesday: lecture
Friday: lecture


HW #5, due by the end of class on the 7th Friday of the semester (Mar. 6): Section 2.5. #2; Section 3.3. #1; Section 3.4. #3, #9, #14

Week 8: sections 5.1, 5.2,
Monday: lecture
Wednesday: lecture
Friday: lecture


HW #6 (previously mis-numbered as HW7), due by the end of class on the 8th Friday of the semester (Mar. 13): Section 5.1. #4, #5, #9.

I will be doing an electronic office hour on Wednesday, March 11, from about 3pm to 4pm. I will be checking my email and Twitter (handle @kay314159) frequently and have my Skype on (kay.kirkpatrick) if you want to contact me.



Week of March 23: sections 5.2, 5.3,
Monday: lecture
Wednesday: lecture
Friday: lecture


HW #7 (OPTIONAL), due Friday, March 27: Section 4.2 #2. Each HW submitted electronically to the grader Timmy Feng mzhdfeng@gmail.com must be a single pdf file.
(Super optional: If you have the bandwidth for some quantum mechanics too, I recommend doing problems 4.1.3 and 4.2.1. Also optional: watch some videos about PDE and Fourier series material. For example:
https://www.khanacademy.org/science/electrical-engineering/ee-signals/ee-fourier-series/v/ee-fourier-series-intro
https://www.khanacademy.org/science/electrical-engineering/ee-signals/ee-fourier-series/v/ee-visualize-fourier-series-square-wave
If you find other well-captioned videos that you like or think I might like, please let me know.)


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.

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