Fourier Series : Fourier series, Theorems, Dirichlet’s conditions, Fourier series for even and odd functions, Half range Fourier series, Other forms of Fourier series
Laplace Transforms : Definition of Laplace transform, linearity property–Piecewise continuous function. Existence of Laplace transform, Functions of exponential order and of class A. First and second shifting theorems of Laplace transform, Change of scale property- Laplace transform of derivatives, Initial value problems, Laplace transform of integrals, Multiplication by t, Division by t, Laplace transform of periodic functions and error function, Beta function and Gamma functions. Definition of Inverse Laplace transform, Linearity property, First and second shifting theorems of inverse Laplace transform, Change of scale property, Division by p, Convolution theorem, Heaviside’s expansion formula (with proofs and applications).