3CE6

ENGINEERING MATHEMATICS

UNIT 1

Fourier Series & Z  Transform –

Expansion of simple functions in fourier series. Half range series, Change

of intervals, Harmonic analysis.

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.