Book:Alexander Graham/Numerical Analysis

Subject Matter

 * Numerical Analysis

Contents

 * Introduction
 * Notation used


 * Finite Differences
 * 1.1 The forward difference operator
 * 1.2 Some other operators and the relations between them
 * 1.3 Differences of polynomial functions
 * 1.4 Errors in difference tables
 * 1.5 Interpolation formulae
 * 1.6 The throwback technique
 * 1.7 Numerical differentiation and integration
 * 1.8 Some formulae for differentiation
 * 1.9 Integration


 * Lagrange Interpolation Polynomial and Divided Differences
 * 2.1 Lagrange interpolation polynomial
 * 2.2 Divided differences
 * 2.3 Newton's interpolation formula with divided differences
 * 2.4 Equally spaced tabular points


 * Simultaneous Linear Equations
 * 3.1 Direct methods
 * 3.2 Computing the inverse of a matrix
 * 3.3 Iterative methods
 * 3.4 Rounding errors and ill-conditioning
 * 3.5 Accumulation of errors in addition (and subtraction)
 * 3.6 Accumulation of errors in multiplication (and division)
 * 3.7 Errors in solving systems of simultaneous equations


 * Numerical Solution of Differential Equations
 * 4.1 Picard's method
 * 4.2 A Taylor series method
 * 4.3 Euler's method
 * 4.4 The Adams-Bashforth method
 * 4.5 The Runge-Kutta method
 * 4.6 Differential equations of order higher than $1$
 * 4.7 Accuracy and stability


 * Non-Linear Equations
 * 5.1 Linear iterations
 * 5.2 Quadratic iterations
 * 5.3 Bairstow's method


 * Conclusion
 * Bibliography
 * Index



Source work progress
* : $\text I$: Finite Differences: $1.1$ The forward difference operator