Linear Algebra. Vector space, subspace and its properties, linear independence and dependence of vector, matrices, rank of matrix, reduction to normal forms, linear homogeneous and non-homogeneous equations, Cayley-Hamilton theorem, characteristic roots and vectors.
Theory of equation. De Moivere’s theorem, relation between roots and coefficient of nth degree equation, solution to cubic and biquadratic equation, transformation of equation.
Diff. calculus. Limit and continuity, differentiability of functions, successive differentiation, leibnitz’s theorem, partial differentiation, Euler’s theorem on homogeneous functions, tangents and normals, asymoptotes, singular points, curve tracing.
Integral calculus. Reduction formulae, integration and properties of definite integrals, quadrature, rectification of curves, volumes and surfaces of solids of revolution.
Linear, homogeneous equation, first order higher degree equations, algebraic properties of solutions, linear homogeneous equation with constant coefficients, solution of second order differential equation, linear non-homogeneous differential equations.
Neighbourhood, open and sets, limit point and Bolzano weirstrass theorem, continuous functions, sequences and their properties, limit superior and limit inferior of a sequence, infinite series and their convergence, Rolle’s theorem, mean value theorem, Taylor’s theorem, Taylor’s series, Maclaurin’s series, maxima and minima, indeterminate forms.
Measures of central tendency and dispersion and their properties, skewness and kurtosis, introduction to probability, theorem of total and compound probability, Bayes theorem, random variables, probability