Linear Algebra: Matrices and Determinants; Inverse and Rank of matrix; Systems of linear equations; Eigen values and Eigen vectors. Cayley-Hamilton Theorem.
Calculus: Limit, continuity and differentiability; Partial Derivatives; Mean value theorems; Indeterminate forms and L Hospitals rule; Maxima and minima; Taylors theorem; Sequences and series; Test for convergence;Fourier series.
Vector Calculus: Gradient; Divergence and Curl; Line; surface and volume integrals; Stokes, Gauss and Greens theorems.
Diferential Equations: Linear and non-linear first order ODEs; Higher order linear ODEs with constant coefficients; Cauchys and Eulers equations.
Probability and Statistics: Measures of central tendency and dispersion; hypothesis testing; Binomial, Poisson, exponential and normal distributions; Correlation and regression analysis.
Numerical Methods: Solutions of linear algebraic equations; Interpolation; Integration of trapezoidal and Simpsons rule; Single and multi-step methods for differential equations.