SOLUTIONS OF EQUATIONS AND EIGEN VALUE PROBLEMS
Newton Raphson method –Iterative method of Gauss -Seidal – Matrix Inversion by Gauss – Jordan method – Eigenvalues of a matrix by power method.
Finite difference – Operators – Properties of operators – Relation between the operators –Interpolation with equal intervals – Newton’s forward and backward difference interpolation – Interpolation with unequal intervals – Lagrange’s and Newton’s divided difference interpolations.
NUMERICAL DIFFERENTIATION AND NUMERICAL INTEGRATION
Approximation of derivatives using interpolation polynomials –Differentiation using interpolation formulae – Numerical integration by Trapezoidal and Simpson’s 1/3rd and 3/8th rules – Double integrals using Trapezoidal and Simpson’s rules.
NUMERICAL SOLUTION OF 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 predictor-corrector methods for solving first order equations.
BOUNDARY VALUE PROBLEMS IN ORDINARY AND PARTIAL DIFFERENTIAL EQUATIONS
Finite difference methods for solving 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 wave equation by explicit method
Reference Book:
1. Gerald C.F. and Wheate, P.O. ,"Applied Numerical Analysis", 2 nd Edition, Pearson Education Asia, New Delhi, 2014. (UNIT-I, II, III, IV ,V).
2. Chapra, S.C and Canale, R.P. “Numerical Methods for Engineers”, 6th Edition, Tata McGraw Hill Edition, 2014 (UNIT-III,IV,V)
3. Grewal, B.S and Grewal, J.S, “Numerical methods in Engineering and Science”, 9th Edition, Khanna Publishers, New Delhi, 2012 (UNIT-III,IV,V)
4. Kreyszig, E., “Advanced Engineering Mathematics”, 8th Edition, John Wiley & Sons, Inc, Singapore, 2008. (Unit I, II, III, IV & V)
5. Kandasamy, P., Thilagavathy. K and Gunavathy, K., "Numerical Methods", 3rd Edition, S.Chand & Company Pvt. Ltd, 2013. (UNIT-I, II, III, IV, V).
Text Book:
1. Veerarjan, T. and Ramachandran.T., "Numerical Methods with programming in ‘C’", Second Edition Tata McGraw Hill Pub.Co.Ltd, First reprint 2007 (UNIT-I, II).
2. Sankar Rao K., "Numerical Methods For Scientists And Engineers", 3rd Edition Prentice Hall of India Private, New Delhi, 2007. (UNIT-I, II, III, IV,V).
