S.Baskar

introduction to numerical AnalysisS. Baskar2 General InstructionsCourse Number :SI 507 Course Title : numerical AnalysisCourse Preliminaries:Continuity of a Function and Intermediate Value Theorem; Mean ValueTheorem for Differentiation and Integration; Taylor s Theorem (1 and 2 dimensions). Analysis:Floating-Point Approximation of a Number; Loss of Significance and Error Propagation;Stability in numerical Systems:Gaussian Elimination; Pivoting Strategy; LU factorization; Residual Corrector Method;Solution by Iteration; Conjugate Gradient Method; Ill-Conditioned Matrices, Matrix Norms; Eigenvalue prob-lem - Power Method; Gershgorin s Equations:Bisection Method; Fixed-Point Iteration Method; Secant Method; Newton Method;Rate of Convergences; Solution of a System of Nonlinear Equations; Unconstrained by Polynomials:Lagrange Interpolation; Newton Interpolation and DividedDifferences;Hermite Interpolation; Error of the Interpolating Polynomials; Piecewise Linear and Cubic Spline Interpola-tion; Trigonometric Interpolation; Data Fitting and Least-Squares Approximation and Integration:Difference formulae.

Introduction Numerical analysis is a branch of Mathematics that deals with devising efficient methods for obtaining numerical solutions to difficult Mathematical problems. Most of the Mathematical problems that arise in science and engineering are very hard and sometime impossible to solve exactly.

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