Sources in the Development of Mathematics
Series and Products from the Fifteenth to the Twentyfirst Century
£84.99
 Author: Ranjan Roy, Beloit College, Wisconsin
 Date Published: August 2011
 availability: In stock
 format: Hardback
 isbn: 9780521114707
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The discovery of infinite products by Wallis and infinite series by Newton marked the beginning of the modern mathematical era. It allowed Newton to solve the problem of finding areas under curves defined by algebraic equations, an achievement beyond the scope of the earlier methods of Torricelli, Fermat and Pascal. While Newton and his contemporaries, including Leibniz and the Bernoullis, concentrated on mathematical analysis and physics, Euler's prodigious accomplishments demonstrated that series and products could also address problems in algebra, combinatorics and number theory. In this book, Ranjan Roy describes many facets of the discovery and use of infinite series and products as worked out by their originators, including mathematicians from Asia, Europe and America. The text provides context and motivation for these discoveries, with many detailed proofs, offering a valuable perspective on modern mathematics. Mathematicians, mathematics students, physicists and engineers will all read this book with benefit and enjoyment.
Read more Presents the evolution of mathematics starting around 1650 that researchers in various areas will read with benefit and enjoyment
 Traces the origins of many ideas in applied areas, which will be of interest to applied mathematicians, scientists and engineers
 Provides detailed proofs for numerous important theorems and formulas
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×Product details
 Date Published: August 2011
 format: Hardback
 isbn: 9780521114707
 length: 994 pages
 dimensions: 262 x 186 x 50 mm
 weight: 1.88kg
 contains: 44 b/w illus. 379 exercises
 availability: In stock
Table of Contents
1. Power series in fifteenthcentury Kerala
2. Sums of powers of integers
3. Infinite product of Wallis
4. The binomial theorem
5. The rectification of curves
6. Inequalities
7. Geometric calculus
8. The calculus of Newton and Leibniz
9. De Analysi per Aequationes Infinitas
10. Finite differences: interpolation and quadrature
11. Series transformation by finite differences
12. The Taylor series
13. Integration of rational functions
14. Difference equations
15. Differential equations
16. Series and products for elementary functions
17. Solution of equations by radicals
18. Symmetric functions
19. Calculus of several variables
20. Algebraic analysis: the calculus of operations
21. Fourier series
22. Trigonometric series after 1830
23. The gamma function
24. The asymptotic series for ln Γ(x)
25. The Euler–Maclaurin summation formula
26. Lseries
27. The hypergeometric series
28. Orthogonal polynomials
29. qSeries
30. Partitions
31. qSeries and qorthogonal polynomials
32. Primes in arithmetic progressions
33. Distribution of primes: early results
34. Invariant theory: Cayley and Sylvester
35. Summability
36. Elliptic functions: eighteenth century
37. Elliptic functions: nineteenth century
38. Irrational and transcendental numbers
39. Value distribution theory
40. Univalent functions
41. Finite fields.
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