# Mathematics (MATH) 476

## Partial Differential Equations (Revision 1) Revision 1 is closed for registrations, see current revision

Delivery Mode: Individualized study online

Credits: 3

Area of Study: Science

Prerequisite: MATH 270, MATH 365, MATH 366, and MATH 376, from Athabasca University; or equivalent courses from another institution. Professor approval is required to register in this course.

Faculty: Faculty of Science & Technology

MATH 476 is not available for challenge.

## Overview

Mathematics 476: Partial Differential Equations considers significant topics in this area of mathematics (see the unit list, below).

## Outline

Mathematics 476 consists of the four units listed below:

• Unit 1: The Diffusion / Heat Equation
• Unit 2: The Wave Equation in One Dimension
• Unit 3: Higher-dimensional Partial Differential Equations
• Unit 4: Fourier and Laplace Transform Solutions of Partial Differential Equations

## Learning Outcomes

Upon successful completion of this course, you should be able to

• demonstrate understanding of the meaning of a partial differential equation (PDE), its order and solution; the concepts of initial and boundary conditions; and initial boundary value problems (IBVPs).
• use physical laws such as the Fourier’s law of heat conduction, Fick’s law of diffusion, Newton’s law on a vibrating string, and the conservation of thermal energy to derive the heat/diffusion, wave, and Laplace equations, respectively.
• solve initial boundary value problems for the heat/diffusion, wave and Laplace equations subject to different boundary conditions, using Fourier series and separation of variables.
• use the method of characteristics to solve the initial value problem for the wave equation on an infinite one-dimensional string, a semi-infinite string, and a vibrating string of fixed length.
• demonstrate understanding of the main properties of the Sturm-Liouville eigenvalue problem and of the concept of fundamental solution.
• describe how the properties of the Fourier, Fourier sine, Fourier cosine and Laplace transforms are used to solve some partial differential equations.

## Evaluation

To receive credit for Mathematics 476, you must achieve a minimum grade of D (50 percent) on the final examination, and an overall grade of D (50 percent) for the entire course. The weighting of the composite grade is as follows:

Activity Weighting
Assignment 1 7.5%
Assignment 2 7.5%
Assignment 3 7.5%
Assignment 4 7.5%
Final Exam 70%
Total 100%

To learn more about assignments and examinations, please refer to Athabasca University's online Calendar.

## Course Materials

### Textbooks

Haberman, Richard. Applied Partial Differential Equations with Fourier Series and Boundary Value Problems (5th ed.). Upper Saddle River, NJ: Pearson Education Inc., 2012.

### Other Materials

The course materials also include an online study guide and a course manual.

Athabasca University reserves the right to amend course outlines occasionally and without notice. Courses offered by other delivery methods may vary from their individualized-study counterparts.

Opened in Revision 1, April 30, 2013.