Description
Principle of Mathematical Induction, Recall of Binomial Theorem for positive index, General and Middle terms in Binomial expansions, Properties of Binomial coefficients, Binomial Theorem for any index, Summation of infinite Binomial series.
Solution of Trigonometric Equations, Sine, Cosine and Projection formulae for triangles, De Moivre’s theorem, applications of De Moivre’s theorem including primitive nth root of unity. Expansions of sin nθ , cos nθ , , (n∈N). The exponential, logarithmic, direct and inverse circular and hyperbolic functions of a complex variable.
Recall of determinant of a matrix, Properties of determinants, Hermitian and skew-Hermitian matrices, linear dependence of row and column vectors, row rank, column rank and rank of a matrix and their equivalence.
Theorems on consistency of a system of linear equations (both homogeneous and non-homogeneous). Eigen-values, eigen-vectors and characteristic equation of a matrix, Cayley-Hamilton theorem and its use in finding inverse of a matrix. Diagonalization.
