Definition and solution of ordinary differential equation, first order ordinary deferential equation, first order ordinary differential equation with constant co-efficient. Initial value problems and their application. Besselís equations, and function series solutions.
Definition of Laplace transform, Laplace transform of different functions, First shift theorem, inverse transform, Linearity, use of first shift theorem and partial functions. Transform of derivatives, Transform of an integral, The Heaviside unit function, the unit impulse function. The second shift theorem, Periodic functions, Convolution, solution of ordinary differential equations by Laplace transform.
Fourier series, convergence of Fourier series, Fourier analysis, Fourier transforms.