Steffensen J. Interpolation 2006
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Steffensen J. Interpolation 2006
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Textbook in PDF format
This Dover edition, first published in 2006, is an unabridged republication of the second edition of
the work originally published in 1950 by Chelsea Publishing Company, New York. The first edition
was published in 1927 by The Williams & Wilkins Company, Baltimore.
In the mathematical subfield of numerical analysis, interpolation is a procedure that assists in "reading between the lines" in a set of tables by constructing new data points from existing points. This rigorous presentation employs only formulas for which it is possible to calculate error limits.
Table of contents:
1. Introduction
2. Displacement-Symbols and Differences
3. Divided Differences
4. Interpolation-Formulas
5. Some Applications
6. Factorial Coefficients
7. Numerical Differentiation
8. Construction of Tables
9. Inverse Interpolation
10. Elementary Methods of Summation
11. Repeated Summation
12. Laplace's and Gauss's Summation-Formulas
13. Bernoulli's Polynomials
14. Euler's Summation-Formula
15. Lubbock's and Woolhouse's Formulas
16. Mechanical Quadrature
17. Numerical Integration of Differential Equations
18. The Calculus of Symbols
19. Interpolation with Several Variables
20. Mechanical Cubature
Appendix