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Math 257/316: Partial Differential Equations

### Class Venues, Times, and Instructor Information:

**Section 102:**

Monday, Wednesday, Friday at 9 am in Geography 200.

Instructor: Dr. Jessica Conway.

E-mail: conway@math.ubc.ca

Office hours: Math Annex 1110 - Mondays 12-2pm, Fridays 12-1pm.

Problem Sessions: Chemistry Building Rm 250 - Mondays 5:30-7pm.

### Course Information:

Course outline here.

Office hours for all Math 257/316 instructors and TAs: Grid

### Dates to Remember:

**Midterm 1:** Monday, October 19th.
**Midterm 2:** Friday, Novermber 20th.
**Final Exam:** After December the 7th on a date at a time and location TBA.

### Class Demos:

Excel Spread Sheet to evaluate a Fourier Series
Falstad Demos
Oboe
Heat0, Laplace0, Wave0, HeatFS_TDBC, Heat0f

### Online Excel/Calc Spreadsheet Tutorials:

Obtaining a spread sheet
Basic Excel Tutorial, Basic Calc Tutorial
Using Excel to evaluate a Fourier Series
Using Excel to solve the Heat Equation by Finite Differences
Comparing the Finite Difference solution of the Heat Equation with the Fourier Series Solution
Using Excel to solve the wave equation - including how to construct a slider
Using Excel to solve Laplace's Equation

### Handouts and WEB Resources:

Math 257/316 Course Notes by Richard Froese
Notes on the Radius of Convergence
Additional worked-out heat equation examples
Additional Eigenfunction Expansion Examples (assignment from last year): Supplementary Examples, Solutions

### Lecture Notes:

- Introduction to Partial Differential Equations
- Preliminaries
- Series Solutions of differential equations
- Introduction to computation using spreadsheets
- Fourier Series and separation of variables:
- Heat Equation: Lecture 10, Lecture 11, Lecture 12, Lecture 19, Lecture 20, Lecture 21, Lecture 22
- Fourier Series: Lecture 13, Lecture 14, Lecture 15, Lecture 16
- Wave Equation: Lecture 23, Lecture 24, Lecture 25
- Laplace Equation: Lecture 26, Lecture 27, Lecture 28, Lecture 29, Lecture 30

- Boundary value problems and Sturm-Louiville Theory:

### Old Midterms and Exams:

- Midterm 1:
- Midterm 2:
- Final Exam:

### Homework:

Assignment 1, Solutions
Assignment 2, Solutions
Assignment 3, Solutions
Assignment 4, Solutions
Assignment 5, Solutions
Assignment 6, Heat0Slider0H.xls, Heat0Slider0H_SliderFails.xls; Solutions, Solved Spreadsheet
Assignment 7, Heat_Assg7prob3.xls; Solutions, Solved Spreadsheet
Assignment 8, Heat_Assg8Prob4.xls; Solutions to problems 2, 3, 4, Solved Spreadsheet
Assignment 9, Wave_Assg9.xls; Solutions, Solved Spreadsheet

### Suggested Problems from Textbook:

__Section 5.2:__ 7a, b
__Section 5.3:__ 8, 12
__Section 5.4:__ 6, 7, 8, 23, 24, 44, 45, 46
__Section 5.5:__ 1, 3, 8, 13
__Section 5.6:__ 6, 10
__Section 10.1:__ 16
__Section 10.2:__ 13, 16
__Section 10.4:__ 15a, 16a
__Section 10.5:__ 7, 11
__Section 10.6:__ 1, 4, 7

Jessica M. Conway / Department of Mathematics /
University of British Columbia
Last modified: Thurs Sept 4 14:15:15 PDT 2008