Syllabus For Numerical Analysis

Syllabus for Numerical Analysis Third Class Physics Department College of Science Chapter One: Introduction 1-1 Numerical; Computational Modeling 1-2 Numerical Representation and Error 1-3 Error Analysis 1-3-1 Chopping off and Rounding off error 1-3-2 Truncation Error 1-3-3 Formulation Error 1-4 Accuracy and Precision Chapter Two: Numerical Solution of Non-Linear Equation 2-1 Locating the Position of Roots 2-2 Bisection Method 2-3 False Position Method 2-4 Secant Method 2-5 Simple Iterative by Algebraic Transformation (Fixed Point) 2-6 Sufficient Condition for Convergence 2-7 Accelerating Convergence (Aitken Method) 2-8 Newton-Raphson Method 2-9 Deflated Newton-Raphson Method 2-9 Equations with Nearly Equal Roots 2-10 Birge-Vieta Method 2-11 System of Non-Linear Equations 2-11-1 Fixed Point Iteration for Nonlinear System 2-11-2 Newton-Raphson Method for Nonlinear System Chapter Three: Interpolation and Curve Fitting 3-1 Interpolation and Extrapolation 3-2 Finite Differences and Difference Operators 3-3 Gregory Newton Forward Interpolation Method

3-4 Gregory Newton Backward Interpolation Method 3-5 Central Difference Interpolation Methods 3-5-1 Gauss Backward Formula 3-5-2 Gauss Forward Formula 3-5-3 Stirling’s Formula 3-5-4 Bessel’s Formula 3-5 Divided Difference Formula 3-6 Lagrange Interpolation 3-7 List Square Fitting 3-9 Polynomial Fitting 3-8 Exponential and Curve Fitting Chapter Four: Numerical Integration 4-1 The Trapezoidal rule 4-2 The Simpson's 1/3 rule 4-3 The Simpson's 3/8 rule 4-4 Error in Trapezium, Simpsons rules. 4-5 Higher Order Integration Formulae 4-6 Romberg Integration 4-7 Close and Open Integration Formulae Chapter Five: Numerical Derivation 5-1 Fires Derivation 5-1-1 Forward Difference Approximation 5-1-2 Backward Difference Approximation 5-1-3 Central Difference Approximation 5-1-4 Five Point Formula 5-2 Second, and Higher Order by Difference Formula 5-3 Partial Differentiation Formulas 5-2 Derivation from Difference Table 5-3 Derivation of The Lagrange Polynomial Chapter Six: Solution of Ordinary differential equation 7-1 Euler's Method 7-2 Multi-Step Methods 7-2-1 Adams-Bashforth Formulae 7-2-2 Adams-Molton Formulae 7-2-3 Predictor-Corrector Methods

7-2 Taylor Series Method 7-3 Power Series Solutions of Initial Value Problems 7-4 Picard’s Method 7-5 Runge-Kutta Method 7-6 Finite-Difference Method Chapter Seven: Numerical solution of linear system 7-1 Gaussian Elimination Method 7-2 Triangular Factorization 7-3 LU-Decompositions 7-4 Gauss Jordan Method 7-5 Iterative Jaccobi Method 7-6 Iterative Gauss-Seidel Method 7-7 Successive over Relaxation Reffrences [1] John H. Mathews, and Kurtis D. Fink, “Numerical Methods using Matlab”, Fourth Edition, Pearson Education, Inc.,(2004). [2] J. Stoer, and R. Bulirsch, “Introduction to Numerical Analysis”, Second Edition, Springer-Verlag New York, Inc. (1993). [3] Steven T. Karris, ”Numerical Analysis using Matlab and Spreadsheets”, Second Edition, Orchard Publications, (2004).