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Transforms and Partial Differential Equations objectives is to introduce Fourier series analysis which is central to many applications in engineering apart from its use in solving boundary value problems as well as to acquaint the student with Fourier transform techniques used in wide variety of situations and also to introduce the effective mathematical tools for the solutions of partial differential equations that model several physical processes and to develop Z transform techniques for discrete time systems.

Transforms and Partial Differential Equations Syllabus:

Unit I Partial Differential Equations

Formation of partial differential equations – Singular integrals — Solutions of standard types of first order partial differential equations – Lagrange‟s linear equation — Linear partial differential equations of second and higher order with constant coefficients of both homogeneous and non-homogeneous types.

Unit II Fourier Series

Dirichlet‟s conditions – General Fourier series – Odd and even functions – Half range sine series – Half range cosine series – Complex form of Fourier series – Parseval‟s identity – Harmonic analysis.

Unit III Applications of Partial Differential Equations

Classification of PDE – Method of separation of variables – Solutions of one dimensional wave equation – One dimensional equation of heat conduction – Steady state solution of two dimensional equation of heat conduction (excluding insulated edges).

Unit IV Fourier Transforms

Statement of Fourier integral theorem – Fourier transform pair – Fourier sine and cosine transforms – Properties – Transforms of simple functions – Convolution theorem – Parseval‟s identity.

Unit V Z – Transforms and Difference Equations

Z- transforms – Elementary properties – Inverse Z – transform (using partial fraction and residues) – Convolution theorem – Formation of difference equations – Solution of difference equations using Z – transform.

TOTAL (L:45+T:15): 60 PERIODS

The previous years question paper for the Transforms and Partial Differential Equations is attached in the file below

Transforms and Partial Differential Equations Question Paper