Description
Principle of Mathematical Induction (both strong and weak forms) and its applications, Binomial Theorem for positive index, verification of its correctness by using induction principal, its combinatorial interpretation, Properties of binomial coefficients, Binomial Theorem for any index, summation of infinite binomial series.
Solution of trigonometric equations, sine, cosine and projection formulae for arbitrary 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). Exponential, logarithmic, circular (direct and inverse) and hyperbolic functions of a complex variable.
Determinant of an n´n matrix and its properties. Definition and properties of hermitian and skew-hermitian matrices. Row and column vectors, linearly dependent and independent vectors, row rank, column rank and their equivalence, rank of a matrix. Rank of product of matrices and rank of sum of matrices.
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.
