ALGEBRA & TRIGONOMETRY
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De-Moivre’s theorem and its applications, Square root of complex number. Inverse circular and hyperbolic functions. Logarithm of complex quantity. Summation of series. C+iS methods based on binomial, Geometric, Exponential, sin x and cos x.
Unit II
Definition of rank of a matrix. Theorems on consistency of a system of linear equations. Application of matrices to a system of linear (homogeneous and non-homogeneous equations). Eigen values, Eigen vectors and characteristic equation of a matrix. Caley Hamilton’s theorem
Unit III
Relation between roots and coefficients of a general polynomial equation in one variable, Transformation of equations. Descarte’s rule of signs. Solution of cubic equations (Cardon’s method).
Unit IV
Divisibility, Definition and elementary properties. Division Algorithm, G.C.D. and L.C.M. of two integers, Basic properties of G.C.D., Euclidean algorithm. Primes. Euclid’s theorem. Unique factorization theorem.
