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Full Description
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.
Contents
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.
