|
Unit1.
LAPLACE TRANSFORM: Laplace transform with its simple properties,
applications to the solution of ordinary and partial differential
equations having constant coefficients with special reference to wave and
diffusion equations, digital transforms.
Unit2. FOURIER TRANSFORM: Discrete Fourier transform, Fast Fourier
transform, Complex form of Fourier transform and its inverse applications,
Fourier transform for the solution of partial differential equations
having constant coefficients with special reference to heat equation and
wave equation.
Unit3. FOURIER SERIES: Expansion of simple functions in Fourier
series, half range series, change of interval, harmonic analysis.
CALCULUS OF VARIATION: Functional, strong and weak variations, simple
variation problems, Euler’s equation
Unit4. 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.
Unit5. COMPLEX VARIABLES: Taylor’s series, Laurent’s series, poles,
Residues. Evaluations of simple definite real integrals using the theorem
of residues. Simple contour integration.
|