SYLLABUS

MA25C03 Transforms and its Applications

Laplace Transforms: 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.

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.

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.

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.
Weightage: Continuous Assessment: 40%, End Semester Examinations: 60%.
Assessment Methodology: Assignment (20%), Software activity (20%), Quiz (10%),