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This book is based on a course of introductory lectures that I have given for a number of years in Cambridge. I hope that it will be useful not only to students but also more generally to those who need to make use of a digital computer for scientific and engineering purposes. I have endeavoured to give the subject a modern slant and to confine myself to essentials.
The longest chapter is that on interpolation. This is not because of the practical importance of interpolation as such (it is, in fact, a rare operation to perform in a digital computer) but because the idea of the interpolating polynomial is fundamental to the use of finite difference methods in numerical analysis generally. The chapter on interpolation should, therefore, be regarded as laying the theoretical foundations for what is to follow.
The role of Numerical Analysis in Science and Engineering
Iteration
Interpolation
Numerical Integration and Differentiation
Numerical Solution of Ordinary Differential Equations
Problems Reducible to Simultaneous Equations
Solution of Linear Algebraic Equations