MATH 285 "Partial Differential Equations"

Syllabus: linear partial differential equations (linear first-order equations, classification of second-order equations), the wave equation (uniqueness, domain of dependence, characteristic lines, and conservation of energy), Green's function and Sturm-Liouville problems, Fourier series and Fourier integral, the heat equation (uniqueness and the maximum principle), Laplace's equation (the maximum principle, the fundamental solution, and the associated Green's function).

Prerequisites: (MATH 164 and MATH 165) or MATH 174.

Textbook: Eutiquio C. Young, "Partial Differential Equations - An Introduction", Allyn and Bacon, 1972.

Course philosophy

This rigorous upper-division undergraduate course requires a substantial time commitment and consistent engagement through problem solving and class participation. Students are strongly encouraged to take full advantage of office hours.

Grading: homework (40%), first exam (30%), second exam (30%).

Homework

Homework is usually assigned weekly on Wednesday, starting 1/28, and it is due back the following Thursday by 23:59. There will be 11 assignments from which the best 9 will count toward your grade. Late homework is not accepted.

The homework should be uploaded to Gradescope as a single PDF file.

Exams

Both exams are in-class tests. They are scheduled for 3/4 and 4/29, with review sessions to be held on 3/2 and 4/27, respectively. The first exam will be based on material covered from the start of the semester all the way to and including the lecture on 2/25. The second exam will be based on material covered from after the spring break all the way to and including the lecture on 4/22.

Course policies

1. The course average is not based on a curve, nor on previously fixed scales. It will reflect how well the class is doing, and it will be high if everyone is working hard for the homework and is performing well on the exams.

2. Incomplete "I" grades are almost never given. The only justification is a documented serious medical problem or a genuine personal/family emergency. Falling behind in this course or problems with workload on other courses are not acceptable reasons.

3. If you miss one of the exams with a valid excuse (e.g., illness or emergency), you must notify the instructor and provide supporting documentation verifying your excuse as soon as possible. For a valid excuse with supporting documentation, the other exam will count as your make-up test. If you miss both exams, you are in danger of failing the class. In principle, no make-up exams will be offered. If you miss an exam without a valid excuse (and supporting documentation), you will receive a score of 0 on that test.

4. You are responsible for knowing and abiding by the University of Rochester's academic honesty policy. Any violation of academic honesty will be pursued according to the specified procedures. Direct copying of answers from A.I. tools is not allowed and considered academic dishonesty. Furthermore, the following Mathematics Department policy also applies to this class:

       Any usage whatsoever of online solution sets or paid online resources 
       (chegg.com or similar) is considered an academic honesty violation and 
       will be reported to the Board on Academic Honesty. In particular, any 
       assignment found to contain content which originated from such sources 
       is subject to a minimum penalty of zero on the assignment and a full letter 
       grade reduction at the end of the semester (e.g. a B would be reduced to a C). 
       This applies even if the unauthorized content was obtained through indirect 
       means (through a friend for instance) and/or the student is seemingly unaware 
       that the content originated from such sources. If you have any questions about 
       whether resources are acceptable, please check with your instructor.

5. This course follows the College credit hour policy for four-credit courses. This course meets 3 academic hours per week. Students may also be expected to deepen their understanding of the course material through close examination/evaluation of the readings assigned in the course.

Tentative weekly schedule