CBCGS [2017 - current]

CBGS [2013 - 2016]

Old [2000 - 2012]

## Topics with syllabus and resources

100.00 Complex Variable and Mapping

- Functions of a complex variable, Analytic functions, Cauchy-Riemann equations in Cartesian co-ordinates, Polar co-ordinates.
- Harmonic functions, Analytic method and Milne Thomson methods to find f(z), Orthogonal trajectories.
- Conformal Mapping, Linear, Bilinear transformations, Cross ratio, fixed points and standard transformation such as rotation and magnification, invertion, translation.

200.00 Laplace Transform

- Introduction, Definition of Laplace transform, Laplace transform of constant, trigonometrical, exponential functions.
- Important properties of Laplace transform:- First shifting theorem, Laplace transform without proof.
- Unit step function, Heavi side function, Dirac-delta function, Periodic function and their Laplace transforms, Second shifting theorem.
- Inverse Laplace transform with Partial fraction and Convolution theorem (without proof).
- Application to solve initial and boundary value problem involving ordinary differential equations with one dependent variable and constant coefficients.

300.00 Fourier Series

- Dirichlet’s conditions, Fourier series of periodic functions with period 2π and 2L.
- Fourier series for even and odd functions.
- Half range sine and cosine Fourier series, Parsevel’s identities (without proof).
- Orthogonal and Ortho-normal functions, Complex form of Fourier series.
- Fourier Integral Representation.

400.00 Vector Algebra and Calculus

- Vector Algebra:- Scalar and vector product of three and four Vectors and their properties.
- Vector Calculus:- Vector differential operator, Gradient of a scalar point function, Diversions and Curl of Vector point function.
- Vector Integration:- Line integral; conservative vector field, Green’s theorem in a plane (Without proof)
- Gauss-Divergence theorem & Stokes’ theorem (Without proof and no problems on verification of above theorems).

500.00 Z Transform

- Z-transform of standard functions such as Z(a
^{n}), Z(n^{p}). - Properties of Z-transform:- Linearity, Change of scale, Shifting property, Multiplication of K, Initial and final value, Convolution theorem (all without proof)
- Inverse Z transform:- Binomial Expansion and Method of Partial fraction.