Sources in the Development of Mathematics: Series and Products from the Fifteenth to the Twenty-first Century

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Cambridge University Press, 13 de juny 2011
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.
 

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Continguts

The Taylor Series
1
6
Series and Products for Elementary Functions
The Calculus of Operations
Quaternions
Fourier Series
Trigonometric Series after 1830

4
The Rectification of Curves
Inequalities
Geometric Calculus
6
8
9
Interpolation and Quadrature
The Gamma Function
The Asymptotic Series for ln Γx
Sums of Powers of Integers
The EulerMaclaurin Summation Formula
Integration of Rational Functions
Infinite Product of Wallis
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Sobre l'autor (2011)

Ranjan Roy is the Ralph C. Huffer Professor of Mathematics and Astronomy at Beloit College. Roy has published papers and reviews in differential equations, fluid mechanics, Kleinian groups, and the development of mathematics. He co-authored Special Functions (2001) with George Andrews and Richard Askey, and authored chapters in the NIST Handbook of Mathematical Functions (2010). He has received the Allendoerfer prize, the Wisconsin MAA teaching award, and the MAA Haimo award for distinguished mathematics teaching.

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