Assignments:

No	Due Date	Exercises	Solutions
1	Jan 15 4PM	1.1, 2.2.9, 2.3.8, 2.4.3(2)	sol-1
2	Jan 21 4PM	2.5.1(1)-(4), 2.5.12, 3.2.3, 3.2.4, 3.4.3	sol-2
3	Jan 28 4PM	3.5.1, 3.5.5, 3.5.6(use 3.5.5), 3.6.3, 3.6.7	sol-3, maple-file
4	Feb 4 4 PM	4.3.1, 4.3.6, 4.3.10, 4.3.18	sol-4
5	Feb 11 4PM	4.4.2.(1) and (2), Hillen1: Find the Fourier sine and cosine series for cos(3/5 x) on [0,5*Pi]. 4.4.5., 5.2.5., 5.3.2.(2)(if you have no mathematical software package, then no graph is needed)	sol-5
6	Mar 03 4PM	5.3.3., 5.4.2.(2), 5.5.3.(3), 5.6.1.	sol-6
7	Mar 10 4PM	6.3.5., 7.2.2, 7.2.9., (as usual, if you have no software to plot these functions, then no graph is needed)	sol-7
8	Mar 17 4PM	8.2.2, 8.2.3, 8.2.6, 8.3.3, 8.3.5	sol-8
9	Mar 24 4PM	10.2.11, 10.2.12(2) deVries et al: Ex 1.1.4.	sol-9
10	Mar 31 4PM	11.2.1(3), 11.2.2., 11.2.3., 11.2.5(5), 11.4.1(5), 11.4.4	sol-10

Text:

M.K. Keane, A very applied first course in Partial Differential Equations, Prentice Hall, New Jersey, 2002.

CORRECTIONS

Course Notes:

1. Introduction

Midterm: Wednesday, Feb 25, 2004, 10-10:50 AM in BSM 145.

Midterm Material: Section 1-5 inclusive.

A nice and helpful webpage: http://staff.aes.rmit.edu.au/peter/FOURIER.HTML
A "Midterm preparation package" can be found on my office door CAB 575. Please copy AND RETURN.
The Review-questions are posted.
The Midterm grades are online (WebCT), average 72.2%.

6. Calculus of Fourier series

(6.1), (6.2), (6.3) Differentiation of Fourier series

(6.4) Integration of Fourier Series

7. Separation of variables II

(7.2) Nonhomogeneous Equations

(7.2) ... continued

(7.3) Nonhomogeneous Boundary Conditions

(7.4) Nonhomogeneous Equation and Nonhomogeneous Boundary Conditions

8. Sturm-Liouville eigenvalue problems

(8.1), (8.2) Regular Sturm-Liouville eigenvalue problem

(8.3) The Rayleigh quotient

(8.4) Generalized Fourier series solutions

10. Classical PDE problems

(10.2) Laplace equation in polar coordinates

(10.*) Fishers Equation (from "A Short Course in Mathematical Biology", by G. de Vries, T. Hillen, M. Lewis, J. Mueller, B. Schoenfisch. to appear in SIAM 2004.)

11. Transform Methods

(11.2) The Fourier Integral Example(maple)
(11.4) The Fourier Transform
(11.5) Solutions of PDE's with Fourier Transform
(11.5) .... Wave equation and Poisson equation

(11.3) Laplace Transform Tables of Laplace Transform short(pdf), long (html)

(11.3) ... PDE examples

Final exam: Friday, April 16, 9-11 AM,

Pavillon, Rows 26 and 28

Review questions
Solutions to the Review questions
Tables for Laplace transform and Fourier transform will be provided during the exam, if applicable.
No calculators are allowed.
A nice and helpful webpage: http://staff.aes.rmit.edu.au/peter/FOURIER.HTML

.... have a nice summer !

Outline

Web-page:

Course notes will be posted on WebCT. I will also post solutions to the assignments

and I will use WebCT for grading.

Syllabus:

Introduction to partial differential equations; classification into parabolic, elliptic, hyperbolic; boundary conditions; the heat-equation, the diffusion equation, the Laplace equation and the wave equation; method of characteristics; separation of variables; Fourier series solutions; Sturm--Liouville eigenvalue problems; Laplace transform methods; Fourier transform methods; applications.

Tentative schedule:

Jan 5	J 7	J 9	J 12	J 14	J 16	J 19	J 21	J 23	J 26	J 28	J 30
1 2.1-2	2.3 2.4	2.5	3.1-3	3.4	3.5	3.6	4.1-2	4.3	4.4	5.1-2	5.3

Feb 2	F 4	F 6	F 9	F 11	F 13	F 23	F 25	F 27	Mar 1	M 3	M 5	M 8
5.3-4	5.4	5.5	5.5-6	Review	Midterm	6.1-3	6.4	7.1-2	7.3	7.3	7.4	7.4

M 10	M 12	M 15	M 17	M 19	M 22	M 24	M 26	M 29	M 31	Apr 2	A 5	A 7
8.1-2	8.4	10.1-2	10.4	10.6	11.1-2	11.2.2	11.4	11.5	11.3	11.3	11.3	Review

Grading:

Homework

20%

Midterm exam: ~~Friday February 13, 2004~~

Wednesday, Feb 25, 2004, 10-10:50 AM in BSM 145.

30%

Final exam: Friday April 16, 2004, 9 AM (location TBA)

50%

Deferred Exam: Saturday May 15, 2004, 9AM-12noon, CAB 243

No calculators are allowed during the exams.

There will be no marks for class participation or in class presentations.

Contact:

Dr. Thomas Hillen, 492-3395, thillen@ualberta.ca
office hours: Tuesday 3-4, Wednesday 2-3 in CAB 575, or by appointment.

Homework:

There will be 10 homework assignments of equal weight. For each student the best 9 assignments will be used to find the homework grade.

The assignments are due on Wednesdays at 4PM in the assignment box, third floor in CAB. No late assignments will be accepted. I encourage you to work in teams of two. If you work in teams of two it will not be considered as dishonesty or cheating (see last item of the outline). But each student has to hand in all solutions.

Grading Scheme:

To assign the grades in the new four-point system I will use the following scheme as recommended by the University of Alberta for a third year course:

A+(6%), A(8%), A-(10%), B+(11%), B(16%), B-(15%), C+(13%), C(7%), C-(5%), D+(3%), D(3%), F(3%)

I reserve the right to adjust the scale upwards, as to give better grades.

Policies:

Policy about course outlines can be found in Section 23.4(2) of the University Calendar.

Academic honesty:

The University of Alberta is committed to the highest standards of academic integrity and honesty. Students are expected to be familiar with these standards regarding academic honesty and to uphold the policies of the University in this respect. Students are particularly urged to familiarize themselves with the provisions of the Code of Student Behavior (online at www.ualberta.ca/secretariat/appeals.htm) and avoid any behavior which could potentially result in suspicions of cheating, plagiarism, misinterpretation of facts and/or participation in an offence. Academic dishonesty is a serious offence and can result in suspension or expulsion from the University.

Math 337 Q1

Introduction to Partial

Differential Equations