FIRST SEMESTER MTMP-10l CLASSICAL ALGEBRA & TRIGONOMETRY Full Marks : 51 Pass Marks: (To answer one question from each u...
FIRST SEMESTER
MTMP-10l
CLASSICAL ALGEBRA & TRIGONOMETRY
Full Marks : 51
Pass Marks:
(To answer one question from each unit. Each unit will have provision for internal choice
GROUP-A
CLASSICAL ALGEBRA
(Marks —30)
Unit —I
Marks-li
Adjoint of a square matrix, Jacobi’s Theorem; Inverse of a square matrix, Elementat ransformation on matrices, Rank of a matrix, Solution of a system of linear equations matrix inverse and by Gaussian elimination method.
Unit —II
Marks-10Relation between the roots and coefficients of a polynomial equation of nth degree v. special reference to cubic equations, Symmetric function of roots; Transformation of equations. Cardan’s Method of solution of cubic equation of the form ax3+bx+c=O (a O); Inequality involving Arithmetic and Geometric means.
Unit —III
Marks-10Sequences and their convergence and divergence , Monotqnic and Bounded Sequence are the theorems involving them; Infinite series of constant term; Convergence and divergence r the series of positive terms; Tests of convergence- Comparison test, D-Alembert’s ratio te. Raabe’s test, Cauchy’s root test (without proof).
GROUP-B
TRIGONOMETRY
(Marks-20)
Unit -IV
Marks-10De’ Moivre’s theorem (for rational indices), Expansions of sin nO & cos nO, Expansions:
sinO & cos 0 in ascending powers of 0, Functions of complex arguments.
Unit -V
Marks-10Gregory’s series; summation of trigonometric series; Hyperbolic functions.
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