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| Topics | ||||||||||||||||||
| Numerical solution of nonlinear equations:� fixed point iteration, bisection, false position, Newton-Raphson, and secant method. | ||||||||||||||||||
| Solution of linear systems:� Gaussian elimination and pivoting, LU factorization. | ||||||||||||||||||
| Interpolation and approximation: Lagrange polynomials, piecewise Langrange interpolation, splines, parametric interpolation, multidimensional interpolation, curve fitting, least squares method. | ||||||||||||||||||
| Numerical differentiation:� finite differences form interpolation, finite differences from Taylor series, matrix representation of finite difference schemes. | ||||||||||||||||||
| Numerical integration: Newton-Cotes formula, trapezoidal rule, Simpson?s rule, error analysis, Richardson?s extrapolation and Romberg integration, adaptive quadrature. | ||||||||||||||||||
| Numerical solution of ordinary differential equations:� initial value problems, Runge-Kutta type formulas, predictor-corrector methods, system of differential equations, boundary value problems, higher order differential equations. | ||||||||||||||||||
| Numerical solution of partial differential equations:� hyperbolic equations, parabolic equations, and elliptic equations, finite-difference equations. | ||||||||||||||||||
| Textbook | ||||||||||||||||||
| Mathews, John H.,� Numerical Methods for Mathematics, Science, and Engineering, 2nd Ed.,� Prentice Hall, Englewood Cliffs, NY. | ||||||||||||||||||
| References | ||||||||||||||||||
| Hamming, Richard W., Numerical Methods for Scientists and Engineers, 2nd Ed., McGraw-Hill,� NY. | ||||||||||||||||||
| Conte, S.D. and Carl de Boor,� Elementary Numerical Analysis;� An Algorithmic Approach,� McGraw-Hill, NY. | ||||||||||||||||||
| .......list of required Algorithms | ||||||||||||||||||