Integral Transforms & Partial Differential Equations (MAL201)
Laplace Transforms: Definition of Laplace Transforms, Linearity property, condition for existence of Laplace Transform, first and second shifting properties, transforms of derivatives and integrals, evaluation of integrals by Laplace Transform. Inverse Laplace Transform, convolution theorem, Laplace Transform of periodic functions, unit step function and Dirac delta function. Applications of Laplace Transform to solve ordinary differential equations.
Fourier Series and Fourier Transforms: Fourier series, half range sine and cosine series expansions, exponential form of Fourier series.
Fourier integral theorem, Fourier transform, Fourier Sine and cosine Transforms, Linearity, scaling, frequency shifting and time shifting properties, convolution theorem.
Z-transform: Z – transform, Properties of Z-transforms, Convolution of two sequences, inverse Z-transform, Solution of Difference equations.
Partial differential equations: Formation of first and second order equations, Solution of first order linear equations: Lagrange’s equation, particular solution passing through a given curve. Higher order equations with constant coefficients, classification of linear second order PDEs, method of separation of variables, Solution of One dimensional wave equation, heat equation, Laplace equation ( Cartesian and polar forms), D’Alembert solution of wave equation.