## Mathematics 3FF3: Partial Differential Equations (Winter, 2019)

### Course Information

Course Objectives: This course introduces students to the study of Partial Differential Equations (PDEs) primarily through an in depth examination of the simplest and most important PDEs that arise in the sciences: the wave equation, the heat equation, and Laplace's equation. Each of these classical equations is considered for the most part in the plane, where the differences in the underlying structure of solutions are most clearly exposed. The interplay between the mathematical solutions to these equations and their physical interpretations plays a crucial role in understanding the theory. The principle of causality in the wave equation, the maximum principle in the heat equation, and the mean value theorem in Laplace's equation are just a few important examples of this symbiotic relationship that contributes to making the solving of PDEs a most exciting and rewarding application of mathematics to the sciences. Linear algebra and calculus both play a critical role in solving PDEs.

Topics: First order equations, well-posedness, characteristics, wave equation, heat equation, Laplace equation, boundary conditions, Fourier series, applications.

Instructor:
Dr. Dmitry Pelinovsky, HH-422, ext.23424, e-mail: dmpeli@math.mcmaster.ca
Office hours: Tuesday, Wednesday (13:30-14:30), or by appointment.

Teaching Assistant:
Elkin Ramirez, HH-105, ext. 24336, e-mail: ramireze@mcmaster.ca

Hours:
Lectures: Tuesday, Wednesday, Friday (12:30-13:20); HH-109

Textbook:
"A Course on Partial Differential Equations" by W. Craig (AMS, 2019), ISBN 978-1-4704-4292-7
"Partial Differential Equations. An Introduction" by W. Strauss, 2nd edition (Wiley, 2007), ISBN 978-0-470-05456-7

Assignments: There will be 5 assignments to be completed during the term. Due dates and solutions will be posted on the course webpage. No late assignments will be accepted. Four out of five best marks will be counted in the marking scheme. You may discuss problems of the assignments with each other, but we expect you to write up the answers by yourself. You may not copy another student's solution.

Mid-term Tests: There will be two mid-term tests tentatively scheduled on Wednesday February 13 and Friday March 22 in class time. More information, including the topics covered, will be announced on the course webpage. You must bring your student ID to the test room. In case of a missed test, its percentage will be transferred and added to that of the final exam.

Final Exam: The course is completed by a 2.5-hour final examination. The final exam will be scheduled and administered by the registrar's office.

Marking scheme:
Final exam - 50%
Mid-term tests (2) - 40%
Assignments (4) - 10%

Important message: The instructors and University reserve the right to modify elements of the course during the term. The University may change the dates and deadlines for any or all courses in extreme circumstances. If either type of modification becomes necessary, reasonable notice and communication with the students will be given with explanation and the opportunity to comment on the changes. It is the responsibility of all students to check their McMaster email accounts and course webpages weekly during the term and to note any changes.

Academic Dishonesty: Your attention is drawn to the documents "Senate Statement on Academic Ethics" and "Senate Resolutions on Academic Dishonesty" which you have received during registration and which can be obtained from the Senate Office. Infringements on the rules and principles in these documents will be dealt with in the manner stated therein.

Academic dishonesty is to knowingly act or fail to act in a way that results or could result in unearned academic credit or advantage. This behaviour can result in serious consequences, e.g., the grade of zero on an assignment, loss of credit with a notation on the transcript (notation reads: "Grade of F assigned for academic dishonesty"), and/or suspension or expulsion from the university.

It is your responsibility to understand what constitutes academic dishonesty. For official information on what constitutes academic dishonesty please refer to the written copy of the document Academic Integrity Policy. The following illustrates only three forms of academic dishonesty:
(i) Plagiarism, e.g., the submission of work that is not one's own or for which other credit has been obtained.
(ii) Improper collaboration in group work.
(iii) Copying or using unauthorized aids in tests and examinations.

Requests for Relief for Missed Academic Term Work: Occasionally, students have to miss classes, assignments, or tests because of medical or personal non-medical reasons. Students should review and follow the Academic Regulations in the Undergraduate Calendar with respect to McMaster student absence form (MSAF)

Requests for Relief for Missed Academic Term Work or for absences from classes lasting up to 3 days due to minor medical or personal reasons: Using the McMaster Student Absence Form (MSAF) on-line, self-reporting tool, undergraduate students may report absences lasting up to 3 days and may also request relief for missed academic work. The submission of supporting documentation is not required. Students may use this tool to submit a maximum of one request for relief of missed academic work per term. Students must immediately follow up with their course instructors regarding the nature of the relief. Failure to do so may negate the opportunity for relief. It is the prerogative of the instructor of the course to determine the appropriate relief for missed term work in his/her course.

For medical or personal situations lasting more than three calendar days, and/or for missed academic work worth 25% or more of the final grade, and/or for any request for relief in a term where the MSAF has been used previously in that term: Students must report to their Faculty Office to discuss their situation and will be required to provide appropriate supportingdocumentation. If warranted, the Faculty Office will approve the absence, and the instructor will determine the appropriate relief.

Additional information: Discussions about homework assignments and computer labs are allowed and are generally beneficial. However, you must write up the solutions of the assignment problems by yourself and in your own words. Copying with minor changes (e.g. with symbols changed, or with slightly different wording) from solutions prepared by another person, publication, or website, in whatever format, will be dealt with as an act of plagiarism.