Transforms and Partial Differential Equations

MA6351
CSE EEE EI CIVIL MECH ECE

Unit 1

PARTIAL DIFFERENTIAL EQUATIONS

+ 3 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. I

Part A (2m) Part B (16m)

Unit 2

FOURIER SERIES

+ 3 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. I

Part A (2m) Part B (16m)

Unit 3

APPLICATIONS OF PARTIAL DIFFERENTIAL EQUATIONS

+ 3 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).

Part A (2m) Part B (16m)

Unit 4

FOURIER TRANSFORMS

+ 3 Statement of Fourier integral theorem – Fourier transform pair – Fourier sine and cosine transforms – Properties – Transforms of simple functions – Convolution theorem – Parseval’s identity.

Part A (2m) Part B (16m)

Unit 5

Z - TRANSFORMS AND DIFFERENCE EQUATIONS

+ 3 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.

Part A (2m) Part B (16m)
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