3EE6.1 MATHEMATICS

Unit-1

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.

Unit-2

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.

Unit-3

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

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. Evaluations of simple

definite real integrals using the theorem of residues. Simple contour integration.