Overview
Mathematics 476: Partial Differential Equations considers significant topics in this area of mathematics (see unit list below).
Outline
Mathematics 476 consists of the four units listed below:
- Unit 1: The Diffusion / Heat Equation in One Dimension
- 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 (IBVP).
- 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 | Weight |
| 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.
Materials
Digital course materials
Links to the following course materials will be made available in the course:
Haberman, R. (2013). Applied partial differential equations with Fourier series and boundary value problems (5th ed.). Pearson Education.
Other Materials
Mathematics 476 also includes an online course orientation and study guide.