Laplace transform, The Laplace transform of a periodic function, Heaviside’s
expansion theorem, Convolutions, Integral equations, Transfer functions,
Green’s function and Indical admittance, The Z transform, Inverse Z
transform, Solution of difference equations, Stability of discrete-time systems,
The strum-Liouville problem, Eigenvalues and Eignfunctions, Orthognality of
eigenfunctions, Expansion in series of eigenfunctions, Legendre’s equation,
Bessel’s equation, The wave equations, The vibrating string, Cauchy problem,
Separation of variables, D’Alembert’s Formula, Numerical solution of the
wave equation. Laplace’s equation, Boundary conditions, Numerical solution of Laplace’s equation. Linear algebra, Cramer’s rule, Row Echelon form and
Gaussian elimination, Eigenvalues and eigenvectors, Systems of linear
differential equations.