Series and Products in the Development of Mathematics: Volume 1
eBook - PDF

Series and Products in the Development of Mathematics: Volume 1

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

Series and Products in the Development of Mathematics: Volume 1

About this book

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.

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Yes, you can access Series and Products in the Development of Mathematics: Volume 1 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. Frontispiece
  4. Title page
  5. Copyright information
  6. Contents
  7. Contents of Volume 2
  8. Preface
  9. 1 Power Series in Fifteenth-Century Kerala
  10. 2 Sums of Powers of Integers
  11. 3 Infinite Product of Wallis
  12. 4 The Binomial Theorem
  13. 5 The Rectification of Curves
  14. 6 Inequalities
  15. 7 The Calculus of Newton and Leibniz
  16. 8 De Analysi per Aequationes Infinitas
  17. 9 Finite Differences: Interpolation and Quadrature
  18. 10 Series Transformation by Finite Differences
  19. 11 The Taylor Series
  20. 12 Integration of Rational Functions
  21. 13 Difference Equations
  22. 14 Differential Equations
  23. 15 Series and Products for Elementary Functions
  24. 16 Zeta Values
  25. 17 The Gamma Function
  26. 18 The Asymptotic Series for ln Γ(x)
  27. 19 Fourier Series
  28. 20 The Euler–Maclaurin Summation Formula
  29. 21 Operator Calculus and Algebraic Analysis
  30. 22 Trigonometric Series after 1830
  31. 23 The Hypergeometric Series
  32. 24 Orthogonal Polynomials
  33. Bibliography
  34. Index