1. Theory of complex variables:
Analytic functions, Cauchy-Riemann equation, harmonic functions, line integral, Cauchy's
theorem and Cauchy's integral, simple form of conformal transformation with application of the solution of two
dimensional problems.
2. Finite differences and difference equations :
Finite differences, interpolation, Newton's and Lagrange's formula, difference equation with constants co-efficient, solution of ordinary and partial differential equations with boundary conditions by finite difference method.
3. Numerical methods :
Roots of algebric equations, solution of linear simultaneous equations, numerical differentiation and integration,
numerical methods to solve first order; first degree ordinary differential equations.
4. Laplace transforms :
Definition, Laplace transform of elementary functions, properties of Laplace transform, inverse Laplace
transform, transform of derivatives, transform of integration, multiplication by
tn, division by t, convolution theorem, unit-step and heaviside's unit function, dirac-delta function, periodic functions, solution of ordinary linear differential equations, simultaneous equation with constant co-efficient applied to electrical circuits.
5. Fourier series :
Definition of periodic function, Euler's formula, functions having points of discontinuity, change of intervals, odd
and even functions, expansion of odd or even periodic functions, half range sine and cosine series, elements of harmonic analysis.
6. Fourier transforms :
Definition, Fourier integral, Fourier sine and cosine integration, complex form of
Fourier integral, Fourier transform, Fourier sine and cosine transform, inverse Fourier
transforms.
7. Statistics :
Probability, Total probability, Independent
events, theorem of compound probability, Bay's theorem, random variable, discrete probability distribution,
continuous probability distribution, expectation, moment generating function, repeated trials, Binomial, Poisson's and normal distribution applications, calculation of errors, probable error, standard error.
* Books:
1 Applied Mathematics vol-I & II by P.N.Wartikar & J.N.Wartikar.
2 Higher Engineering Mathematics by B.S.Grewal.
3 Engineering mathematics by Shrivastva.
4 Text Book of Engineering Mathematics by A.B.Mathur &
V.P.Jaggi.
