Mathematics(1st semester)
Group A(Classical algebra)
Unit I:Adjoint of square matrix, Jacobi’s Theorem, Inverse of a square matrix, Elementry transformation of a matrices, Rank of matrix, Solution of a system of linear equation by matrix inverse and by Gaussian elimination method.
Unit II:Relation between the roots and coefficients of a polynomial equation of nth degree with special refrence to cubic equations, Symmetric functions of roots, Transformation of equation, Cardan’s Method of solution of cubic equation of the form ax3+bx+c=0(a≠0), Inequalities involving Arithmatic and Geometric mean.
Unit III: Sequence and their convergence and divergence, Monotonic and bounded sequences and the theorem involving them, Infinite series…………., Convergence and Divergence of the series of positive terms, Test of convergence-comparison test, D-Alembert’s ratio test, Raabe’s test, Cauchy’s root test(without proof).
Group B(Trigonometry)
Unit IV: De’ Moiver’s theorem(for rational indices), Expansion of sin nϴ& cos nϴ, Expansion of sinϴ & cosϴ in ascending powers of ϴ, Functions of complex arguments.
Unit V: Gregory’s series, summation of trigonometric series, Hyperbolic functions.
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