MATH 331: Partial Differential Equations Spring 2019

Course Topics Review of ordinary differential equations (Sections 0.1 - 0.2) Boundary value problems for ODE (Sections 0.3 - 0.4) Fourier series; Fourier integral; convergence (Chapter 1) Heat equation; the product method (Sections 2.1 - 2.6) Sturm-Liouville problems; eigenfunctions series (Sections 2.7 - 2.13) Wave equation: product method solution; D’Alembert’s solution (Chapter 3) Potential equation; harmonic functions (Chapter 4) Higher dimensions, other coordinates, applications (selected sections of Chapter 5) Laplace and Fourier transform methods (Chapter 6 and handouts) Numerical methods; Monte-Carlo method (selected sections of Chapter 7) The tentative schedule of the course has been posted on my website; see http://home.sandiego.edu/~pruski/m331s19schedule.html

Course Learning Outcomes Upon successful completion of this course, the student will: Demonstrate a working knowledge of the theory of second-order linear partial differential equations, including the knowledge of theorems with assumptions. Be able to: solve simple boundary value problems for ordinary differential equations, determine Fourier series and Fourier integral of simple functions, apply the product method, transform method, and selected numerical methods to solve standard initial-boundary value problems for heat, wave, and potential equations. Demonstrate the ability to: solve problems in the topics listed above, including applications from the field of physics and engineering, use a computer environment, such as MATLAB, to solve differential equations and visualize and interpret the solutions, understand simple proofs and write elementary proofs, communicate mathematical ideas clearly.

Attendance, Proofs, Textbook, MATLAB Regular attendance is really necessary. It is quite difficult to catch up with the material when you miss a class. It may become virtually impossible, if you miss several classes. Proofs: One of the most important tasks in mathematics is proving that certain statements are true. We will be doing proofs in class and you will be required to do simple proofs in your assignments and during the exams. The textbook: Powers, Boundary Value Problems and Partial Differential Equations. Sixth Edition. This is one of the best textbooks I have used in my life: serious yet accessible to students. There is not enough time to lecture on everything in class, so you will have to learn some material on your own. Reading the assigned material is absolutely essential! Pop quizzes will include questions on the assigned reading as a gentle method of enforcing your reading. MATLAB: The course will include a MATLAB® component. It is a high-level language and interactive environment that enables you to perform computationally intensive tasks, including solving differential equations, analyzing the solutions, and visualizing them. Some homework assignments will contain a MATLAB component. You are also encouraged to use MATLAB or other resources to avoid tedious computations in your homework assignment exercises.

Office Hours and Contact Office hours (Dr. Lukasz Pruski, Serra 147, x. 4035): Monday 2:30 – 4:00 Tuesday 3:00 – 4:00 Wednesday 3:30 – 5:00 Friday 12:20 – 1:20 and at other times, by appointment. (I may not be available on some Thursdays.) Contact: The best way to contact me is by using e-mail (pruski@sandiego.edu or lukaszpruski@gmail.com). I read e-mail many times a day. I have voice mail (x. 4035), but I often forget to check it. If for some reason you are unable to contact me, try calling our departmental Executive Assistant, Tina Manabat, at extension 4706.

Assignments, Quizzes, Project Homework Assignments will be assigned and collected with frequency yet to be determined (decision by class vote). For many of the assigned exercises, a BOB (back of the book) answer will be available. The total homework assignment score will count for 25% of the course grade. Late assignments will not be accepted unless you have a valid reason and you arrange it with me in advance. This semester I am teaching two upper-division courses and I have to do all the grading myself, so expect severe delays. Pop-quizzes (not announced in advance). There will be 8 - 10 of them. Quiz questions will refer to the recently covered material and to the new material you were supposed to read. Two or three lowest quiz scores will be dropped, and the remaining scores will count for 25% of the course grade. Quizzes cannot be made up unless you have a valid reason for not taking the quiz and you notify me in advance of your absence. Research project requiring team research will be assigned in April to be completed by May 10. Each project requires a write-up; volunteers will be solicited to present their projects in class. The project counts for 5% of the course grade.

Exams Midterm (Friday, March 15). The test is of the closed-book variety. No advanced calculators, smart phones, iPads, iPods or similar gadgets are allowed. The test score will count for 15% of the course grade. A test can be made up only if you have an actual emergency and if you notify me in advance about your absence. The Final exam (Friday, May 17, 2:00 – 4:30) will be cumulative and its score will count for 30% of the course grade. The final exam will also be closed book, and no advanced calculators or any electronic gadgets will be allowed.

Grading Criteria Total percentage Grade ============== ===== ============== ===== 92% and above A 90% - 92% A- 88% - 90% B+ 82% - 88% B 80% - 82% B- 75% - 80% C+ 65% - 75% C 60% - 65% C- 50% - 60% D Note: I will “curve grades up” in the unlikely case when the number of A’s and B’s falls below about 40% of the current enrollment.

Academic Integrity Academic integrity is strongly promoted by the Department of Mathematics. I hope issues related to academic integrity will not arise in our course. There have been some cases of cheating in math/computer science courses in the past – copying someone else’s work or cheating during exams. Depending on the severity of the case, the possible consequences include: assigning the score of 0 on the given assignment, lowering the course grade, or even assigning F in the course.