TRANSFORMS AND ITS APPLICATIONS
                                               (Common to EEE, EIE, ICE branches)
 Module – I: Laplace transform
Existence conditions, Properties of Laplace transform, Laplace
transform of standard functions, derivatives and integrals, Unit step
function and Dirac delta function, Laplace transform of periodic functions;
Inverse Laplace transform: Partial fraction technique, Convolution theorem.
Application: Solution of second order ordinary differential equations
using Laplace transform.
 Activities: Compute the Laplace transform of time-domain functions,
Inverse Laplace transform, Solution of ordinary differential equations using
Laplace transform.

 Module – II: Z-transform
Z-transform of standard functions, properties: Inverse Z-transform:
Standard functions, Partial fraction technique, Convolution theorem.
Application: Solution of difference equation using Z-transform.
Activities: Compute the Z-transform of a discrete-time signal, Solution
of linear constant-coefficient difference equations using Z-transform.

  Module – III: Fourier series
Dirichlet’s conditions, General Fourier series, Convergence of Fourier
series, Odd and even functions; Half range sine series, Half range cosine
series, Root mean square value, Parseval’s identity.
Application: Solution of one-dimensional wave and heat equation.
Activities: Compute Fourier coefficients, Reconstruct signal using
Fourier series (Partial sum), Plot convergence of Fourier series.

Module – IV: Fourier transform
Complex Fourier transform, Properties, Relation between Fourier and
Laplace transform, Fourier sine and cosine transforms, Parseval’s identity,
Convolution theorem.
Application: Simple applications to solve partial differential equations
using Fourier transform.
Activities: Compute the Fourier and inverse Fourier transform,
Parseval’s theorem validation.