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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.

UNIT V:- Numerical integration and solution of ordinary differential equations:-
Trapezoidal rule – Simpson’s 1/3rd and 3/8th rule – Solution of ordinary differential equations by Taylor’s series – Picard’s method of successive approximations – Euler’s method – Runge-Kutta method (second and fourth order).