RTU 3rd sem Electronics And Communication Engineering B.Tech. Syllabus Advanced Engineering Mathematics I

3EC6A Advanced Engineering Mathematics I

Unit I

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 II

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 III

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 specialreference to heat equation and wave equation.

Unit IV

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 V

COMPLEX VARIABLES -Taylor’s series Laurent’s series poles, Residues,
Evaluation of simple definite real integrals using the theorem of residues. Simple
contour integration.