APM346, Fall 2016


APM346 - Fall 2016
Lecturer Jonathan Korman Office: PG307A email: jkorman at math dot toronto dot edu Office Hours: Tue 3-4pm and by appointment Lecture L0101 Wed 2-4 pm in KP 108 Thr 10-11am in LM 162 Tutorials (Krishan) T0101: Thr 12-13 in BA 1200 T0301: Wed 16-17 in MP134	Teaching Assistants Krishan Rajaratnam Office: BA 6283 email: kr dot rajaratnam at mail dot utoronto dot ca Office Hours: Mon 11am-1pm (every week) Tristan Milne Office: BA 6283 email: tristan dot milne at mail dot utoronto dot ca Office Hours: Fri 1-2pm (on Oct 14, 28: 11am-12pm).

General Info

The suggested textbook is: "Partial Differential Equations: An Introduction" by Walter A. Strauss. Any edition. Can be found at the UT bookstore, in libraries, or purchased online. The textbook is suggested as supplementary reading but is not required. Another book used in the recent past for this course is: "Applied Partial Differential Equations, with Fourier Series and Boundary Value Problems" by Richard Haberman. Prof. Ivrii's online textbook is a valuable resource.

Course Syllabus (approximate):

Strauss textbook: chapters 1-6, 9, 12.
Supplemental material from lectures.

The Course Grade will be calculated as follows:

Homework- 25%
Term Test - 30%
Final Exam - 45%

Homework assignments are to be handed in during tutorials on the assigned dates. Assignments should be handed in at the beginning of your tutorial. Late homework will not be accepted. Please staple your homeworks. Unstapled homeworks will be penalized 2 points.
There will be 5-6 homework assignments. Complete solutions to all homework problems will be posted after due date. For each homework, 2 questions will be randomly selected for grading.

Appealing homework: Concerns about HW grading should be directed to Tristan during his Friday office hour. Alternatively you can request a regrade by turning in your homework together with detailed written concerns back to Krishan during tutorial no later than 1 week after homework has been returned.

Important: There will be no make up term test! If you have a valid reason for missing the term test, the corresponding portion of the final exam will count as your term test grade.

Exam dates:

Term Test: Wed, Oct 26, 2-4pm.
Final Exam: Tue, Dec 13, 7-10pm.

Announcements

There are two independent classes labelled APM346: LEC0101 (Korman) and LEC5101 (Ivrii). The two classes are different: different instructors, different TAs, and different tests. Please do not confuse the two. You must decide by Oct 1 which of the two classes to register in.
Class behaviour: texting or using your laptop disrupts the lecture and distracts other students, therefore it is not allowed.

Tutorials and office hours start on the second week of classes.

Please read the information in the two links below about academic misconduct: Plagiarism, Misconduct.

The official form you must provide in case you missed a term test: requesting special academic consideration.

Course Calendar

# Week of ...

Fall Semester:

1 Sept 14-15 Course information, review of ODEs, introduction to PDEs (degree, linear/non-linear, homogeneous/non-homogeneous), Principle of superposition, auxiliary conditions, well-posed problems.

2 Sept 21-22 1st order linear equations: method of characteristics, types of 2nd order equations, change of coordinates.

3 Sept 28-29 Heat equation. Separations of variables: Heat equation with frozen ends, Heat equation with insulated ends.

4 Oct 5-6 Heat equation. Examples. Qualitative properties: maximum principle, uniqueness and stability of solutions, non-homogeneous problems.

5 Oct 12-13 Fourier Series. Fouries sine and cosine series. Pointwise convergence. Infinite series solutions.

6 Oct 19-20 Fourier Series. Term-by-term differentiation and integration. Heat equation with heat source: series solutions. Laplace equation.

7 Oct 26-27 Midterm. Laplace equation.

8 Nov 2-3 Laplace equation on the disk, qualitative properties: Mean Value property,maximum principle, uniqueness of solutions for BVP, stability,sovability condition. Wave equation. Midterm grades+solutions posted.

9 Nov 9-10 Wave equation on finite interval (separation of variables), formula in terms of initial data, wave eq on line (characteristics), D'Alembert formula, qualitative properties: causality, conservation of energy, uniqueness of solutions.

10 Nov 16-17 Wave eq on half line: reflection. Fourier Transform.

11 Nov 23-24 Fourier Transform. Heat equation on line.

12 Nov 30-Dec 1 Method of characteristics for quasilinear equations. Weak solutions. Traffic at stop light.

#	Week of ...
Fall Semester:
1	Sept 14-15	Course information, review of ODEs, introduction to PDEs (degree, linear/non-linear, homogeneous/non-homogeneous), Principle of superposition, auxiliary conditions, well-posed problems.
2	Sept 21-22	1st order linear equations: method of characteristics, types of 2nd order equations, change of coordinates.
3	Sept 28-29	Heat equation. Separations of variables: Heat equation with frozen ends, Heat equation with insulated ends.
4	Oct 5-6	Heat equation. Examples. Qualitative properties: maximum principle, uniqueness and stability of solutions, non-homogeneous problems.
5	Oct 12-13	Fourier Series. Fouries sine and cosine series. Pointwise convergence. Infinite series solutions.
6	Oct 19-20	Fourier Series. Term-by-term differentiation and integration. Heat equation with heat source: series solutions. Laplace equation.
7	Oct 26-27	Midterm. Laplace equation.
8	Nov 2-3	Laplace equation on the disk, qualitative properties: Mean Value property,maximum principle, uniqueness of solutions for BVP, stability,sovability condition. Wave equation. Midterm grades+solutions posted.
9	Nov 9-10	Wave equation on finite interval (separation of variables), formula in terms of initial data, wave eq on line (characteristics), D'Alembert formula, qualitative properties: causality, conservation of energy, uniqueness of solutions.
10	Nov 16-17	Wave eq on half line: reflection. Fourier Transform.
11	Nov 23-24	Fourier Transform. Heat equation on line.
12	Nov 30-Dec 1	Method of characteristics for quasilinear equations. Weak solutions. Traffic at stop light.

Homework Assignments

HW 1	due Sept 28, Sept 29
HW2	due Oct 12, Oct 13
HW 3	due Nov 2, Nov 3
HW 4	due Nov 16, Nov 17
HW 5	due Nov 30, Dec 1