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Matrices and Determinants, Systems of linear equations, Eigen values and eigen vectors.
Limit, continuity and differentiability; Partial Derivatives; Maxima and minima; Sequences and series; Test for convergence; Fourier series, Taylor series.
Gradient; Divergence and Curl; Line; surface and volume integrals; Stokes, Gauss and Green’s theorems.
Linear and non-linear first order ODEs; Higher order linear ODEs with constant coefficients; Cauchy’s and Euler’s equations; Laplace transforms; PDEs – Laplace, heat and wave equations.
Probability and Statistics:
Mean, median, mode and standard deviation; random variables; Poisson, normal and binomial distributions; correlation and regression analysis; tests of significance, analysis of variance (ANOVA).
Solutions of linear and non-linear algebraic equations; numerical integration – trapezoidal and Simpson’s rule; numerical solutions of ODE.