• Successive Differentiation, Mean Value Theorems and Indeterminate Forms • Applications of Differentiation: Expansion of Functions and Approximations, Curve Tracing, Curvature, Evolutes and Involute, Maxima Minima • Sequences and Series: Convergence and Divergence of Infinite Series, Conditional and Absolute Convergence • Properties of Definite Integrals and Reduction Formulae, Improper Integrals, Beta & Gamma Functions • Applications of Integration—Area, Length, Volume, Surface Area • Multi-variate Differentiation: Partial Differentiation, Euler’s Theorem, Change of Variables • Applications of Multivariate Differentiation: Expansion of Functions of Two Variables, Approximations, Jacobians, Maxima and Minima • Matrices, Determinants, Inverse and Rank of Matrix, Hermitian and Skew-Hermitian Matrices • Solution of System of Equations, Eigen Values, Eigen Vectors, Diagonalizing a Matrix, etc. • Multiple Integration, Double and Triple Integrals and Applications • Fourier Series, Half-Range Series • Vector Differentiation: Gradient, Divergence and Curl • Vector Integration: Line Integral, Surface Integral, Stoke’s Theorem and Gauss’s Theorem • Ordinary Differential Equations of Order One, Linear, Exact, Equations of First Order but not of First Degree, Clairaut’s Equation • Linear Differential Equations of Higher Order, Method of Variation of Parameters and Applications • Series Solution, Bessel’s Differential Equation and Legendre’s Differential Equation • Complex Number System: Complex Functions, Differentiation and Analyticity, Conformal and Bilinear Mapping • Complex Integration: Taylor and Laurent’s Series, Residue Theorem, Evaluation of Real Integrals • Vector Spaces • Basic Statistics • Applied Statistics – Curve Fitting, Correlation and Regression • Theory of Probability • Discrete Probability Distributions • Continuous Probability Distributions • Sampling, Tests of Significance for Large Samples • Tests for Small Samples • Answers and Hints to the Problems in Exercises.