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# Mathematics -II

JNTUK R19 & R20 Mathematics -II  Syllabus & Study notes:-

UNIT-I:- Solving systems of linear equations, Eigen values and Eigen vectors:
Rank of a matrix by echelon form and normal form – Solving system of homogeneous and nonhomogeneous equations linear equations – Gauss Elimination for solving system of equations – Eigen values and Eigen vectors and their properties.

UNIT-II:- Cayley-Hamilton theorem and Quadratic forms:
Cayley - Hamilton theorem (without proof) – Finding inverse and power of a matrix by CayleyHamilton theorem – Reduction to Diagonal form – Quadratic forms and nature of the quadratic forms – Reduction of quadratic form to canonical forms by orthogonal transformation.

UNIT III:- Iterative methods:-
Introduction – Bisection method – Secant method – Method of false position – Iteration method – Newton-Raphson method (One variable and simultaneous Equations) – Jacobi and Gauss-Seidel methods for solving system of equations.

UNIT IV:- Interpolation:-
Introduction – Errors in polynomial interpolation – Finite differences – Forward differences – Backward differences – Central differences – Relations between operators – Newton’s forward and backward formulae for interpolation – Interpolation with unequal intervals – Lagrange’s interpolation formula – Newton’s divide difference formula.