Spring 2025 - APMA 901 G100

Partial Differential Equations (4)

Class Number: 2792

Delivery Method: In Person

Overview

  • Course Times + Location:

    Jan 6 – Apr 9, 2025: Wed, Fri, 10:30 a.m.–12:20 p.m.
    Burnaby

Description

CALENDAR DESCRIPTION:

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.

Grading

  • Homeworks and problem session participation 65%
  • Midterm examination 10%
  • Final examination 25%

NOTES:

Details on the ‘Participation’ component of the grading scheme: There will be regular homework assignments and every 2 weeks we will allocate an additional 1.5 hour for student-led problem solving and discussions based on the assigned problem sets. Many 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.

REQUIREMENTS:

Prerequisites:A solid undergraduate course in PDE(equivalent to SFU’s Math 418), and at least a first course in real analysis (equivalent to SFU’s Math 320). Contact me if you haven’t had these prerequisites.

Materials

REQUIRED READING:

Texts: PDEs is a vast subject, and your class notes will form an important resource. There is no perfect textbook for everyone, and I'm happy to provide you with additional suggestions. You're encouraged to be diligent about note-taking. 
We will broadly follow the sequence of topics in Chapters 1-6 in
Textbook: "Partial Differential Equations" by Lawrence Evans

We will refer to the exposition in 
- An introduction to partial differential equations by Renardy and Rogers (available as an ebook through the SFU library 

REQUIRED READING NOTES:

Your personalized Course Material list, including digital and physical textbooks, are available through the SFU Bookstore website by simply entering your Computing ID at: shop.sfu.ca/course-materials/my-personalized-course-materials.

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.

Registrar Notes:

ACADEMIC INTEGRITY: YOUR WORK, YOUR SUCCESS

SFU’s Academic Integrity website http://www.sfu.ca/students/academicintegrity.html is filled with information on what is meant by academic dishonesty, where you can find resources to help with your studies and the consequences of cheating. Check out the site for more information and videos that help explain the issues in plain English.

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

RELIGIOUS ACCOMMODATION

Students with a faith background who may need accommodations during the term are encouraged to assess their needs as soon as possible and review the Multifaith religious accommodations website. The page outlines ways they begin working toward an accommodation and ensure solutions can be reached in a timely fashion.