Series and Products in the Development of Mathematics: Volume 1

First of two volumes tracing the development of series and products. Second edition adds extensive material from original works.

Ranjan Roy (Author)

9781108709453, Cambridge University Press

Paperback / softback, published 18 March 2021

776 pages
25.2 x 17.6 x 4.2 cm, 1.43 kg

'an impressive source book with original materials from the creators of calculus (with excursions into algebra and number theory) from all over the world.' Pelegr? Viader, MathSciNet

This is the first volume of a two-volume work that traces the development of series and products from 1380 to 2000 by presenting and explaining the interconnected concepts and results of hundreds of unsung as well as celebrated mathematicians. Some chapters deal with the work of primarily one mathematician on a pivotal topic, and other chapters chronicle the progress over time of a given topic. This updated second edition of Sources in the Development of Mathematics adds extensive context, detail, and primary source material, with many sections rewritten to more clearly reveal the significance of key developments and arguments. Volume 1, accessible to even advanced undergraduate students, discusses the development of the methods in series and products that do not employ complex analytic methods or sophisticated machinery. Volume 2 treats more recent work, including deBranges' solution of Bieberbach's conjecture, and requires more advanced mathematical knowledge.

1. Power series in fifteenth-century Kerala
2. Sums of powers of integers
3. Infinite product of Wallis
4. The binomial theorem
5. The rectification of curves
6. Inequalities
7. The calculus of Newton and Leibniz
8. De Analysi per Aequationes Infinitas
9. Finite differences: interpolation and quadrature
10. Series transformation by finite differences
11. The Taylor series
12. Integration of rational functions
13. Difference equations
14. Differential equations
15. Series and products for elementary functions
16. Zeta values
17. The gamma function
18. The asymptotic series for ln ?(x)
19. Fourier series
20. The Euler–Maclaurin summation formula
21. Operator calculus and algebraic analysis
22. Trigonometric series after 1830
23. The hypergeometric series
24. Orthogonal polynomials
Bibliography
Index.

Subject Areas: Popular science [PDZ], History of mathematics [PBX]