This course covers the theory of initial and boundary value problems for linear parabolic, elliptic, and hyperbolic partial differential equations. Topics may include first order equations, second order equations, separation of variables, the Sturm-Liouville problem, transform methods, Green's functions, Fourier series, numerical methods and modeling applications.
- Demonstrate comprehension and capability to derive Fourier series and Fourier transforms.
- Understand basic numerical methods of partial differential equations.
- Understand the Sturm-Liouville theory and its applications.
- Understand the theory and the applications of the wave, the heat, the Laplace, and the Poisson equations in rectangular/polar/cylindrical/spherical coordinates, with boundary values.