Math 337

Introduction to PDEs
 
July 05 - Aug 11, 2010
M T W R F, 12-1:10 PM
CAB 273
 Lizard



Final Marks by ID number

Contents:


  • Classification of PDEs (partial differential equations)
  • Heat equation
  • Wave equation
  • Laplace equation
  • Method of separation of variables
  • Fourier series solutions
  • Method of characteristics
  • D'Alemberts solution
  • Sturm-Liouville problems
  • Fourier transform methods
  • Laplace transform methods (if time allows)

Course Material:
A course on PDE over the summer is quite an adventure. We will have class every day during the week and it is very important that you do not fall behind. I will give out daily problems which you are supposed to do on the given day to make sure you stay on track. These daily problems will not be graded. Additionally you get homework and assignment problems which will be graded.

There will be a
  • Midterm exam (30%) on July 26, in class
  • Final exam (50%) on August  13 at 8 AM !!!
  • Homework problems (20%). Homework is due as indicated in the calendar below at the beginning of class. Late assignments will not be accepted.

Dr. T. Hillen
Mathematical and Statistical Sciences
University of Alberta
CAB 575
2-3395
thillen@ualberta.ca

Office hours: I am available after class until 13:45 for questions and discussion. Further appointments can be made as needed. 

To help me manage my email inbox, please include "MATH 372" in the subject line of any email message you send to me (without it, your message runs the risk of being deleted without being read).



Webpage:
www.math.ualberta.ca/~thillen/summer2010/math337.html

The textbook below is a standard reference for this course, but you do not need to buy it. Drs Leonard, van Roessel and myself are writing a textbook for this course and we will make it available to you online:
Hillen, Leonard, van Roessel: "Partial Differential Equations for Scientists and Engineers, Problem Book 1, 2010.

original version: problem_book3.pdf
corrected version: problem_book4.pdf

Textbook (optional):
Linear Partial Differential Equations for Scientists and Engineeers by Tyn Myint-U, Lokenath Debnath,  Birkhaeuser, 2006.
Date
Contents
 Problem of the day
 Homework
July 05
 Introduction 1.1, 1.2 Classification 13.1 and 13.3
06
 1.3 Side conditions, 1.4 linear PDE
 10.3
07
 Derivation of diffusion equation, 1.5 Steady states
 11.1
08
 1.6 First example of Separation
 12.1
09
 2.1 PWC, 2.2 Even, odd, periodic, 2.3 orthogonal, linear algebra
 10.1 and 15.6
12
 2.4 Fourier series, Exer. 9.16 a)
 10.5
13
 2.5 Convergence, 2.6 Operations on FS, 2.7 Mean Error, 2.8 Complex Form
 10.16
 HW1 due:
17.3, 17.9, 18.3, 18.14
Solutions
14
 3 Separation, Exer. 3.1 heat eq + Neumann, Exer. 3.2 Telegraph
11.7
15
 3.2 Nonhomogeneous
 11.13
16
 (3.3 heat source, as time allows), 9 Method of Characteristics
 14.4
19
 Characteristics -> D'Alembert, Exer 14.12
 12.7 + 12.8
20
 4 Sturm-Liouville problems, 4.3 Eigenfunction expansions
 look over 15.1,
do 15.9
 HW2 due:
17.2, 18.5, 18.6, 18.7, 18.9
Solutions
21
 Examples, Exer 15.15
 11.9
22
 4.3.1 Rayleigh quotient
 11.10
23
 5 Cartesian coords, Exer. 11.11, 5.2 wave eq -> D'Alembert
 review for midterm
26
 Midterm exam in class
Solutions
27
 5.3 Laplace eq
12.13 ...
 HW3 due:
17.1, 17.7, 18.2, 18.8, 18.18
Solutions
28
 5.4 Maximum principle, 5.5 2-D wave eq
 12.13 continued
29
 (5.6 orthogonal eigenfunction in 2-D, can be skipped if needed)
 12.4
30
 6 Cylindrical coords
 12.14 ...
Aug 02
 Heritage day, University closed

03
 6.2 Bessel functions (briefly), 6.3 Heat equation in 2-D
 12.14 conditnued
 HW4 due:
17.4, 17.6, 17.10, 18.11, 18.17
Solutions
04
 Exer 12.18 pie-shaped domain, 8 Infinite domains
 16.11
05
 8.2 Fourier transform, Exer 16.5, 16.13, 16.14
16.3
06
 Examples
 16.4
09
 8.3.1 Error function, Sine cosine transforms, Exer 16.8, 16.9, 16.16
 16.12
10
 (Exer 16.17 if time allows), Review
 Review
 HW5 due:
17.11, 18.1, 18.10, 18.13, 18.15
Solutions
11
 Class cancelled

12


13
 Final Exam, 8:00-10:00 AM,  CAB 273



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

 

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 Behaviour (online at http://www.ualberta.ca/secretariat/appeals.htm) and avoid any behaviour which could potentially result in suspicions of cheating, plagiarism, misrepresentation of facts and/or participation in an offence.  Academic dishonesty is a serious offence and can result in suspension or expulsion from the University.