 2.1.11.6 Book 6 2 Background 1.2 Cosmological 1.2.11 Mathematics Book 8 2.1.11.8 Book 7 - Numerical Analysis

 Step 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 Step 30 31 32 33 34 35 Answers Lectures 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16
 First Steps in Numerical Analysis  by R.J.Hosking, S.Joe, D.C.Joyce, and J.C.Turner Lectures given at Mahidol University by R. Radok during 1985-1997 - Using First Steps by Hosking et al. and Computational Mathematics by B.P. Demidovich & A.Maron as well as other material ERRORS FINITE DIFFERENCES 01 Errors 1 18 Tables 01 Introduction 02 Errors 2 19 Forward. Backward and Central Differences 02 an Algorithm: Continued Fractions 03 Errors 3 20 Polynomials 03 Rational Functions/Power Series 04 Floating Point Arithmetic INTERPOLATION Expansion in Continued Fractions 05 Function Approximation 21 Linear and Quadratic Interpolation 04 Evaluation of Polynomials NON-LINEAR EQUATIONS 22 Newton Interpolation Formula 05 Floating Point Arithmetic 06 Non-linear Equations 1 23 Lagrange Interpolation Formulae 06 Roots of Non-linear Equations 07 Non-linear Equations 2 24 Divided Differences 07 Linear Equations 08 Non-linear Equations 3 25 Inverse Interpolation 08 Special Matrices 09 Method of Simple Iteration CURVE FITTING 09 Gauss Elimination 10 Newton-raphson Iterative Method 26 Least Squares 10 Matrix Inversion SYSTEMS OF EQUATIONS 27 Least Squares and Linear Equations 11 L-U Decomposition 11 Solution by Elimination 28 Splines 12 Shift Operators 12 Errors and Ill-conditioning NUMERICAL DIFFERENTIATION 13 Finite Differences 13 the Gauss-seidel Iterative Method 29 Finite Differences 14 Interpolation 14 Matrix Inversion NUMERICAL INTEGRATION 15 Numerical Integration 15 Use of Lu Decomposition 30 the Trapezoidal Rule 16 Pseudo Code 16 Testing for Ill-conditioning 31 Simpson's Rule THE EIGEN-VALUE PROBLEM 32 Gauss Integration Formula 17 the Power Method ORDINARY DIFFERENTIAL EQUATIONS 33 Single-step Methods Equations 34 Multi-step Methods 35 Higher Order Differential   