Calculus and Its Origins

Overview

Calculus answers questions that had been explored for centuries before calculus was born. Calculus and Its Origins begins with these ancient questions and details the remarkable story of how subsequent scholars wove these inquiries into a unified theory. This book does not presuppose knowledge of calculus, it requires only a basic knowledge of geometry and algebra (similar triangles, polynomials, factoring). Inside you will find the accounts of how Archimedes discovered the area of a parabolic segment, ibn ...
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Overview

Calculus answers questions that had been explored for centuries before calculus was born. Calculus and Its Origins begins with these ancient questions and details the remarkable story of how subsequent scholars wove these inquiries into a unified theory. This book does not presuppose knowledge of calculus, it requires only a basic knowledge of geometry and algebra (similar triangles, polynomials, factoring). Inside you will find the accounts of how Archimedes discovered the area of a parabolic segment, ibn Al-Haytham calculated the volume of a revolved area, Jyesthadeva explained the infinite series for sine and cosine, Wallis deduced the link between hyperbolas and logarithms, Newton generalized the binomial theorem, Leibniz discovered integration by parts, and much more. Each chapter ends with further results, in the form of exercises, by such luminaries as Pascal, Maclaurin, Barrow, Cauchy and Euler.
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Product Details

  • ISBN-13: 9780883855751
  • Publisher: Mathematical Association of America
  • Publication date: 4/12/2012
  • Series: Spectrum Series
  • Edition description: New Edition
  • Pages: 180
  • Product dimensions: 7.17 (w) x 10.24 (h) x 0.55 (d)

Meet the Author

David Perkins teaches mathematics at Luzerne County Community College. He earned his doctorate from the University of Montana in 1995.
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Table of Contents

Preface; 1. The Ancients; 2. East of Greece; 3. Motion; 4. Indivisibles; 5. Quadrature; 6. The Fundamental Theorem of Calculus; 7. Notation; 8. Chords; 9. Zero over zero; 10. Rigor.
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