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  

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