Partial Differential Equations: Course Outline (MAT 412)
At the end of this course the students will be able to learn about the three most important classes of partial differential equations of applied mathematics, that is, the heat equation, the wave equation and Laplace equation. Apply elementary solution techniques and be able to interpret the results and solve specific problems in major area of studies.
- Review of ordinary differential equation in more than one variable partial differential equations (PDEs) of the first order
- Nonlinear PDEs of first order, Applications of 1st order PDEs,
- Partial differential equations of second order,
- Mathematical modeling of heat, Laplace and wave equations, Classification of 2nd order PDEs,
- Boundary and initial conditions,
- Reduction to canonical form and the solution of 2nd order PDEs,
- Technique of separation of variable for the solution of PDEs with special emphasis on Heat,
- Laplace and wave equations. Laplace transform,
- Fourier transform and Hankel transform for the solution of PDEs and their application to boundary value problems.