Sources in the Development of Mathematics
eBook - PDF

Sources in the Development of Mathematics

Series and Products from the Fifteenth to the Twenty-first Century

  1. English
  2. PDF
  3. Available on iOS & Android
eBook - PDF

Sources in the Development of Mathematics

Series and Products from the Fifteenth to the Twenty-first Century

About this book

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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Yes, you can access Sources in the Development of Mathematics by Ranjan Roy in PDF and/or ePUB format, as well as other popular books in Mathematics & History & Philosophy of Mathematics. We have over one million books available in our catalogue for you to explore.

Table of contents

  1. Cover
  2. Half-title
  3. Title
  4. Copyright
  5. Contents
  6. Preface
  7. 1 Power Series in Fifteenth-Century Kerala
  8. 2 Sums of Powers of Integers
  9. 3 Infinite Product ofWallis
  10. 4 The Binomial Theorem
  11. 5 The Rectification of Curves
  12. 6 Inequalities
  13. 7 Geometric Calculus
  14. 8 The Calculus of Newton and Leibniz
  15. 9 De Analysi per Aequationes Infinitas
  16. 10 Finite Differences: Interpolation and Quadrature
  17. 11 Series Transformation by Finite Differences
  18. 12 The Taylor Series
  19. 13 Integration of Rational Functions
  20. 14 Difference Equations
  21. 15 Differential Equations
  22. 16 Series and Products for Elementary Functions
  23. 17 Solution of Equations by Radicals
  24. 18 Symmetric Functions
  25. 19 Calculus of Several Variables
  26. 20 Algebraic Analysis: The Calculus of Operations
  27. 21 Fourier Series
  28. 22 Trigonometric Series after 1830
  29. 23 The Gamma Function
  30. 24 The Asymptotic Series for ln Γ(x)
  31. 25 The Euler–Maclaurin Summation Formula
  32. 26 L-Series
  33. 27 The Hypergeometric Series
  34. 28 Orthogonal Polynomials
  35. 29 q-Series
  36. 30 Partitions
  37. 31 q-Series and q-Orthogonal Polynomials
  38. 32 Primes in Arithmetic Progressions
  39. 33 Distribution of Primes: Early Results
  40. 34 Invariant Theory: Cayley and Sylvester
  41. 35 Summability
  42. 36 Elliptic Functions: Eighteenth Century
  43. 37 Elliptic Functions: Nineteenth Century
  44. 38 Irrational and Transcendental Numbers
  45. 39 Value Distribution Theory
  46. 40 Univalent Functions
  47. 41 Finite Fields
  48. References
  49. Index