Abstract:

Derivation of the wave equation.

D’Alembert solution for an infinite string, wave bouncing from a clamped and a free end of a string.

Well-posedness. Classification of second order linear problems.

Canonical forms. Laplace equation.

Solution of the wave equation on a bounded interval by separations of variables.

Uniqueness of the solution using the energy method. The maximum principle.

Separation of variables to Laplace equation in a rectangular and in a circle.

The heat equation. The maximum principle for the heat equation.

Solution of the inhomogeneous problem.

Solution of partial differential equations using Integral transforms.

Abstract:

Interpolation and approximations methods, error analysis.

Numerical integration, differentiation.

Ordinary differential equations solution, Solutions to non-linear equations.