Unit I: Solution of Nonlinear Equations ———————————— 10 hours

 Review of calculus and Taylor’s theorem
 Errors in numerical calculations
 Trial and error method
 Bisection method
 Newton’s method
 Secant method and their convergence
 Fixed point iteration and is convergence
Unit II: Solution of Linear Algebraic Equations ————————– 10 hours

 Review of the existence of solutions and properties of matrices
 Gaussian Climination method
 Pivoting
 Ill conditioning
 GaussJordan method
 Inverse of matrix using Gauss elimination method
 Method of factorization
 Dolittle algorithm
 Cholesky’s factorization
 Iterative solutions
 Solving eigen value problems using power method
Unit III: NumericalDifferentiation and Integration ——————— 6 hours

 Newton’s differentiation formulas
 Maxima and minima of tabulated function
 Netwon’s quadrature formulas
 Gaussian integration algorithm
 Romberg integration formulas
Unit IV: Interpolation and Approximation ——————————— 8 hours

 Lagrange’s polynomials
 Newton’s interpolation using difference and divided differences
 Cubic spline interpolation
 Least squares method for linear and nonlinear data
Unit V: Solution of Ordinary Differential Equations ——————— 8 hours

 Review of differential equations
 Initial value problem
 Taylor series method picard’s method
 Euler’s method and its accuracy
 Henu’s method
 RungeKutta methods
 Solution of the higher order equations
 Boundary value problems
 Shooting method and its algorithm
Unit VII: Solution of Partial Differential Equations ——————— 6 hours

 Review of partial differential equations
 Deriving difference equations
 Laplacian equation
 Poisson’s equation
 Engineering examples
Text Book:

 C.F. Gerald and P.O. Wheatly: Applied Numerical Analysis, 4th Edition, addison Wesley publishing Company, New York.
Reference Book:

 W. Chency and D. Kinciad: Numerical Mathematics and Computing, 2nd Edition, Brooks Cole Publishing Co, 1985.
 W.H. Press, B.P. Flannery et.al.: Numerical Recipes in C, 1st Edition, Cambridge press, 1988.
 S. Yakwitz and F. Szidarovszky: An Introduction to Numerical Computations, 2nd Edition, Macmillan Publishing Co., New York.