Fall 2022 - APMA 901 G100
Partial Differential Equations (4)
Class Number: 4094
Delivery Method: In Person
First order non-linear partial differential equations (PDEs) and the method of characteristics. Hamilton-Jacobi equation and hyperbolic conservation laws; weak solutions. Second-order linear PDEs (Laplace, heat and wave equations); Green's functions. Sobolev spaces. Second-order elliptic PDEs; Lax-Milgram theorem.
- Homework and problem session participation 50%
- Final exam 50%
Details on the `Homeworks and participation’ component of the grading scheme: There will be bi-weekly homework assignments and every week we will allocate 1 hour for student-led problem solving and discussions based on the assigned problem sets. Most of the assigned problems will be discussed this way, also touching on the relevant theoretical material that pertains to them. Students are expected to either lead a discussion from the board or actively participate from the audience. Solutions to some of the problems, in particular to those problems that have not been sufficiently discussed upon during discussions, will have to be submitted on paper. All assignments will be weighted equally.
A thorough knowledge of advanced calculus and basic real analysis (eg. Rudin: Principles of Mathematical Analysis).
An advanced undergraduate course in PDEs. Topics assumed to be studied previously: Fourier series, Fourier transform, 1D wave equation (D'Alembert solution, reflections), 1D heat equation (diffusion kernel, maximum principle), Laplace's equation (maximum principle, Green's function). Distributions.
Partial Differential Equations, by L.C. Evans, American Mathematical Society, 1998. We will cover most of Chapters 1-6.
REQUIRED READING NOTES:
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Graduate Studies Notes:
Important dates and deadlines for graduate students are found here: http://www.sfu.ca/dean-gradstudies/current/important_dates/guidelines.html. The deadline to drop a course with a 100% refund is the end of week 2. The deadline to drop with no notation on your transcript is the end of week 3.
ACADEMIC INTEGRITY: YOUR WORK, YOUR SUCCESS
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Each student is responsible for his or her conduct as it affects the university community. Academic dishonesty, in whatever form, is ultimately destructive of the values of the university. Furthermore, it is unfair and discouraging to the majority of students who pursue their studies honestly. Scholarly integrity is required of all members of the university. http://www.sfu.ca/policies/gazette/student/s10-01.html