Sequence and series –Convergence tests –Taylor series –Maclaurin’s series –Binomial theorem Fourier series: Definition - Dirichlet conditions – Fourier coefficients – Fourier series for discontinuous functions – Even function and odd function –Half range series –Change of interval and functions having arbitrary period –Parseval’s formula

Introduction - Gradient, divergence and Curl operators – Solenoidal and conservative fields – Green’s theorem –Gauss Divergence theorem –Stoke’s theorem –Transformation of vectors

Definition –Laplace transform of derivatives –First and second shifting theorems –Laplace transform of Heaviside, step and periodic functions –Inverse Laplace transform –Convolution theorem –Solving second order ordinary differential equations with inhomogeneity

Definition –Connection between beta and gamma functions –Application to evaluation of integrals Complex Analysis: Introduction - Functions of complex variable –Limits –Continuous functions –Differentiability – The Cauchy –Riemann equation(in cartesian and polar forms) –Analytic functions –Harmonic functions .

Permutation and Combinations – Probability – Discrete Random variables - Conditional probability –Baye’s theorem –Continuous distribution function –Gaussian, Poisson and Normal distributions – Expectation values - Variance