**MTH ****522: Numerical Analysis**** ****(4)**

**Pre-requisites**: MTH 303 Real Analysis I

Round off errors and computer arithmetic

Interpolation: Lagrange interpolation, divided differences, Hermite interpolation, splines, numerical differentiation, Richardson extrapolation

Numerical Integration: trapezoidal, Simpsons, Newton-Cotes, Gauss quadrature, Romberg integration, multiple integrals

Solution of linear algebraic equations: direct methods, Gauss elimination, pivoting, matrix factorizations

Iterative methods: matrix norms, Jacobi and Gauss-Siedel methods, relaxation methods

Computation of eigenvalues and eigenvectors: power method, householders method, QR algorithm

Numerical solutions of non-linear algebraic equations: bisection, secan and Newton's, zeroes of polynomials

*Suggested Books*:

- R. L. Burden, D. J. Faires,
*Numerical Analysis* - E. K. Blum,
*Numerical**Analysis and Computation*,*Theory and Practice,*Dover, 2010 - S. D. Conte, C. De Boor,
*Elementary Numerical Analysis*,third edition, McGraw-Hill, 1980 - D. M. Young, R. T. Gregory,
*A**Survey of Numerical Mathematics*, volumes 1 and 2, Dover, 1988

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