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UNIT 1 :
LAPLACE TRANSFORM - Laplace transform with its simple properties,
applications to the solution of ordinary and partial differential
equations having constant co-efficients with special reference to the wave
and diffusion equations.
UNIT 2 : FOURIER SERIES & Z TRANSFORM – Expansion of simple
functions in fourier series. Half range series, Change of intervals,
Harmonic analysis. Z TRANSFORM - Introduction, Properties, Inverse Z
Transform .
UNIT3 : FOURIER TRANSFORM - Complex form of Fourier Transform and
its inverse, Fourier sine and cosine transform and their inversion.
Applications of Fourier Transform to solution of partial differential
equations having constant co-efficient with special reference to heat
equation and wave equation.
UNIT 4 : COMPLEX VARIABLES - Analytic functions, Cauchy-Riemann
equations, Elementary conformal mapping with simple applications, Line
integral in complex domain, Cauchy;s theorem. Cauchy’s integral formula.
UNIT 5 : COMPLEX VARIABLES -Taylor’s series Laurent’s series poles,
Residues, Evaluation of simple definite real integrals using the theorem
of residues. Simple contour integration.
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