Series and Products in the Development of Mathematics: Volume 1

ISBN-13: 9781108709453 / Angielski / Miękka / 2021 / 776 str.

Wisconsin) Roy Ranjan (Beloit College

Opis

This second edition of Sources in the Development of Mathematics, now in two volumes, traces the development of series and products from 1380-2000 through the interconnected concepts and results of unsung and celebrated mathematicians. This first volume is accessible to undergraduates, adding extensive context, detail, and primary source material.

Recenzje

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

Spis treści

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 Γ(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.