# Book:Alexander Graham/Numerical Analysis

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## Alexander Graham:

## Alexander Graham: *Numerical Analysis*

Published $\text {1973}$, **Transworld Student Library**

- ISBN 0 552 40013 0.

### Subject Matter

### Contents

*Introduction**Notation used*

- chapter i
**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

- chapter ii
**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

- chapter iii
**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

- chapter iv
**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

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

*Conclusion**Bibliography**Index*

## Source work progress

- 1973: Alexander Graham:
*Numerical Analysis*: $\text I$: Finite Differences: $1.1$ The forward difference operator