APM346 Partial Differential Equations

Fall 2012

Sections

• L0101Y   MWF9 MP 202

  • instructor: James Colliander
  • office: BA6244 (Bahen Centre)
  • phone: 416-978-3645
  • email: colliand@math.toronto.edu
  • office hours: Thu 1:00–2:00, Fri 10:30–11:30

• L5101Y   M6-9 MP 202

  • instructor: Victor Ivrii
  • office: HU1008 (Huron 215)
  • phone: 416-978-4031
  • email: ivrii@math.toronto.edu
  • office hours: Mon 4:00–5:40 (office) and 9:00-9:20 pm (in or near lecture room)

Teaching Assistants

• Martin Muñoz
  • office: HU1027 (215 Huron)
  • phone: 416-946-4008
  • e-mail: martin.munoz@utoronto.ca
  • office hours TBA
• Ioannis Angelopoulos
  • office: SS622 (Sidney Smith)
  • phone: 416-978-2967
  • e-mail:yannis@math.toronto.edu
  • office hours TBA
• Dianel Fusca
  • office: SS622 (Sidney Smith)
  • phone: 416-978-2967
  • e-mail: daniel.fusca@utoronto.ca
  • office hours TBA





Syllabus

Outline

1. PDE Motivations and Context
   • What is a PDE?
   • Where do PDE arise?
   • What are example PDE problems?
   • Scope of APM346
   • First order linear constant coefficient PDE
2. Initial Value Problems on $\mathbb{R}$
   • Wave Equation
   • Diffusion Equation
   • Waves and Diffusion with Forcing; Duhamel’s Formula
3. Boundary Value Problems
4. Fourier Series
5. Harmonic Functions
6. Topics to be determined (Distributions, Calculus of Variations, Economics and Physics Problems, Nonlinear PDE, Numerical Methods?)

2012-2013 Timetable Description

APM346H1 Partial Differential Equations[36L]

Sturm-Liouville problems, Greens functions, special functions (Bessel, Legendre), partial differential equations of second order, separation of variables, integral equations, Fourier transform, stationary phase method. Prerequisite: MAT235Y1/MAT237Y1/MAT257Y1, MAT244H1 Exclusion: APM351Y1 Distribution Requirement Status: This is a Science course Breadth Requirement: The Physical and Mathematical Universes (5)

Learning Resources 

• Online “Textbook”–hypertext by instructors (developing)
• Forum for discussion (coming soon)
• Optional (but useful) Textbooks
  • Partial Differential Equations: An Introduction, by Walter Strauss (Wiley)
  • Elementary Applied Partial Differential Equations, by Richard Haberman (Prentice-Hall)
  • Beginning Partial Differential Equation, by Peter O’Neil (Wiley)
• Last year:
  • Wiki and
  • Forum and

Marking Scheme

• Homework: 20%,
• Term Test 1: 20%, October 16, Tuesday, 16:00--18:00, EX 200
• Term Test 2: 20%, November 15, Thursday, 18:00--20:00, GB 304, GB 404, GB 412
• Final Exam: 40%.

Term Tests

Scopes and other details:

• Term Test 1
• Term Test 2
• Final Exam
• Missed Tests

Home Assignments

There will be about 10 assignments (1 every week). Problem Sets will be posted on the web an Fridays and should be given 10 days later (Monday). Further details on the homework will be provided with the first assignment.

No late homework will be accepted. Precise instructions will be forthcoming.

2011 Assignments

Recipe for Success

The best recipe for success in this course is to go to all lectures and work on them. Try to understand each lecture thoroughly before the next.
Do not be afraid of asking questions. Come to the office hours! Do the problem sets. Do not wait until the night before. Start early!

© 2012 Department of Mathematics, University of Toronto