• Partial Differentiation, Euler’s Theorem, Change of Variables, Expansion of Functions, Approximation, Jacobians, Maxima-Minima • Reduction Formulae, Beta and Gamma Functions, Improper Integrals, Differenitation under Integral sign-Lebreitz’s Rule, Double and Traple Integrals • Ordinary Differential Equations of Order One: Linear, Exact, Equations of First Order but not of First Degre • Linear Differential Equations of Higher Order, Method of Variation of Parameters, Euler Cauchy’s Form Applications • Series Solution of Differential Equations, Bessel’s Functions and Legendre’s Polynomials • Matrices, Determinants, Inverse, Rank, Hermitian and Skew-Hermitian Matrices • Consistency of General System of Simultaneous Equations, Eigen Values, Eigen Vectors, Diagonalizing a Matrix, Vector Spaces • Vector Differentiation: Gradient, Divergence, Curl and Vector Identities • Vector Integration: Line integral, Green Lemma Surface Integrals, Stoke’s Theorem, Divergence Theorem • Complex Number System: Complex Functions, Differentiation and Analyticity, Conformal and Bilinear Mapping • Function of Complex Variable, Analyticity, Conformal and Bilinear Mapping • Complex Integration: Taylor and Laurent’s Series, Residue Theorem, Evaluation of Real Integrals • Laplace Transformation and Its Inverse, Convolution, Solving Differential Equations by L’ Transform Unit Step Function, Impulse Function  • Fourier Series, Half-Range Series, Harmonic Analysis • Fourier Integrals, Fourier Transforms and their Applications • Partial Differential Equations, Formation and Solution to First Order Equations • Partial Differential Equations of Higher Order and Applications • Difference Equations, Z-transform and Solution to Difference Equations by Z-transform • Numerical Solution to Equations in One Variable and Simultaneous Equations • Finite Differences, Divided Differences and Interpolation • Numeric Differentiation and Numeric Integration • Numerical Solution to Ordinary Differential Equations and Partial Differential Equations • Fundamentals of Statistics • Theory of Probability • Discrete Probability Distributions-Binomial and Poisson and Continuous Probability Distribution-Normal • Sampling and Sampling Distribution Test of Hypothesis • Linear Programming • Answers and Hints to the Problems in Exercises