On completion of this subject, students will be expected to be able to:

1. 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).

2. 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.

3. 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.

4. 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.

5. demonstrate understanding of the main properties of the Sturm - Liouville eigenvalue problem and of the concept of

    fundamental solution.

6. describe how the properties of the Fourier, Fourier sine, Fourier cosine and Laplace transforms are used to solve some