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MA8491 NUMERICAL METHODS Lecture Notes Download MA8491 NUMERICAL METHODS Lecture Notes Download
Department  Electrical and Electronics Engineering
Year 2nd year
Semester 4th Semester
University Anna University
Regulation  R2017
Subject Code MA8491
Subject Name NUMERICAL METHODS
Download File MA8491 NUMERICAL METHODS Lecture Notes, Books, Important 2 Marks Question and Answers, 16 Mark Question with Answers, Syllabus & Question Bank

 

 

MA8491 NUMERICAL METHODS Syllabus

UNIT I SOLUTION OF EQUATIONS AND EIGENVALUE PROBLEMS
Solution of algebraic and transcendental equations – Fixed point iteration method – Newton Raphson method – Solution of linear system of equations – Gauss elimination method – Pivoting – Gauss Jordan method – Iterative methods of Gauss Jacobi and Gauss Seidel – Eigenvalues of a matrix by Power method and Jacobi’s method for symmetric matrices.

UNIT II INTERPOLATION AND APPROXIMATION
Interpolation with unequal intervals – Lagrange’s interpolation – Newton’s divided difference interpolation – Cubic Splines – Difference operators and relations – Interpolation with equal intervals – Newton’s forward and backward difference formulae.

UNIT III NUMERICAL DIFFERENTIATION AND INTEGRATION
Approximation of derivatives using interpolation polynomials – Numerical integration using Trapezoidal, Simpson’s 1/3 rule – Romberg’s Method – Two point and three point Gaussian quadrature formulae – Evaluation of double integrals by Trapezoidal and Simpson’s 1/3 rules.

UNIT IV INITIAL VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS
Single step methods – Taylor’s series method – Euler’s method – Modified Euler’s method – Fourth order Runge – Kutta method for solving first order equations – Multi step methods – Milne’s and Adams – Bash forth predictor corrector methods for solving first order equations.

UNIT V BOUNDARY VALUE PROBLEMS IN ORDINARY AND PARTIAL DIFFERENTIAL EQUATIONS
Finite difference methods for solving second order two – point linear boundary value problems – Finite difference techniques for the solution of two dimensional Laplace’s and Poisson’s equations on rectangular domain – One dimensional heat flow equation by explicit and implicit (Crank Nicholson) methods – One dimensional wave equation by explicit method.

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