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UNIT1
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 .
UNIT 2
LAPLACE TRANSFORM - Laplace transform with its simple properties. Unit
step function, Dirac delta function-their Laplace transforms, Inverse
Laplace, transform – convolution theorem, applications to the solution of
ordinary and partial differential equations having constant coefficients
with special reference to wave and diffusion equations.
UNIT 3
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
NUMERICAL ANALYSIS: Difference operation Forward backward and central,
shift and average operators and relation between them. Newton’s forward
and backward differences interpolation formulae. Sterling’s formulae,
Lagrange’s interpolation formula.
Numerical differentiation and integration. Trapezoidal rule, Simpson's one
third and one eighth rule.
UNIT 5
Numerical integration: Numerical integration of ordinary differential
equations of first order, Picards
method, Euler's method & Modified Euler's Method, Mille's method and Ranga
Kutta fourth order method.
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