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MA1251 NUMERICAL METHODS
(Common to IV Semester Elective for Mechanical, Production, Automobile, and
IV Semester core for Metallurgy Mechatronics and Aeronautical)
1. SOLUTION OF EQUATIONS AND EIGEN VALUE PROBLEMS
Linear interpolation methods (method of false position) - Newton’s method - Statement of Fixed Point Theorem - Fixed pointer iteration x=g(x) method - Solution of linear system of Gaussian elimination and Gauss-Jordan methods - Iterative methods: Gauss Jacobi and Gauss – Seidel methods- Inverse of a matrix by Gauss-Jordan method. Eigen value of a matrix by power methods.
2. INTERPOLATION AND APPROXIMATION
Lagrangian Polynomials - Divided difference - Interpolation with a cubic spline - Newton forward and backward difference formulae.
3. NUMERICAL DIFFERENTIATION AND INTEGRATION
Derivatives from difference table - Divided difference and finite difference - Numerical integration by Trapezoidal and Simpson’s 1/3 and 3/8 rules - Romberg’s method - Two and three point Gaussian quadrature formulas - Double integrals using trapezoidal and Simpson’s rules.
4. INITIAL VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS
Single step Methods: Taylor Series and methods - Euler and Modified Euler methods - Fourth order Runge-Kutta method for solving first and second order equations - Multistep methods –Milne’s and Adam’s predictor and corrector methods.
5. BOUNDARY VALUE PROBLEMS
Finite difference solution for the second order ordinary differential equations. Finite difference solution for one dimensional heat equation by implict and explict methods - one dimensional wave equation and two dimensional Laplace and Poisson equations.
TUTORIAL
TEXT BOOKS
1. Gerald, C.F, and Wheatley, P.O, “Applied Numerical Analysis”, Sixth Edition, Pearson Education Asia, New Delhi.2002.
2. Balagurusamy, E., “Numerical Methods”, Tata McGraw-Hill Pub. Co. Ltd., New Delhi, 1999.
REFERENCES
1. Kandasamy, P.Thilakavthy, K and Gunavathy, K. Numerical Methods. S.Chand and Co. New Delhi, 1999
2. Burden, R.L and Faries, T.D., “Numerical Analysis”, Seventh Edition, Thomson Asia Pvt. Ltd., Singapore, 2002.
3. Venkatraman M.K, “Numerical Methods” National Pub. Company, Chennai, 1991.
4. Sankara Rao K., “Numerical Methods for Scientists and Engineers”, 2nd Ed. Prentice Hall India, 2004
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