Table of Contents

Preface.- 1 TRIGONOMETRY.- 1.1 The Hellenic Period.- 1.2 Ptolemy’s Table of Chords.- 1.3 The Indian Contribution.- 1.4 Trigonometry in the IslamicWorld.- 1.5 Trigonometry in Europe.- 1.6 From Viète to Pitiscus.- 2 LOGARITHMS.- 2.1 Napier’s First Three Tables.- 2.2 Napier’s Logarithms.- 2.3 Briggs’ Logarithms.- 2.4 Hyperbolic Logarithms.- 2.5 Newton’s Binomial Series.- 2.6 The Logarithm According to Euler.- 3 COMPLEX NUMBERS.- 3.1 The Depressed Cubic.- 3.2 Cardano’s Contribution.- 3.3 The Birth of Complex Numbers.- 3.4 Higher-Order Roots of Complex Numbers.- 3.5 The Logarithms of Complex Numbers.- 3.6 CasparWessel’s Breakthrough.- 3.7 Gauss and Hamilton Have the FinalWord.- 4 INFINITE SERIES.- 4.1 The Origins.- 4.2 The Summation of Series.- 4.3 The Expansion of Functions.- 4.4 The Taylor and Maclaurin Series.- 5 THE CALCULUS.- 5.1 The Origins.- 5.2 Fermat’s Method of Maxima and Minima.- 5.3 Fermat’s Treatise on Quadratures.- 5.4 Gregory’s Contributions.- 5.5 Barrow’s Geometric Calculus.- 5.6 From Tangents to Quadratures.- 5.7 Newton’s Method of Infinite Series.- 5.8 Newton’s Method of Fluxions.- 5.9 Was Newton’s Tangent Method Original?.- 5.10 Newton’s First and Last Ratios.- 5.11 Newton’s Last Version of the Calculus.- 5.12 Leibniz’ Calculus: 1673–1675.- 5.13 Leibniz’ Calculus: 1676–1680.- 5.14 The Arithmetical Quadrature.- 5.15 Leibniz’ Publications.- 5.16 The Aftermath.- 6 CONVERGENCE.- 6.1 To the Limit.- 6.2 The Vibrating String MakesWaves.- 6.3 Fourier Puts on the Heat.- 6.4 The Convergence of Series.- 6.5 The Difference Quotient.- 6.6 The Derivative.- 6.7 Cauchy’s Integral Calculus.- 6.8 Uniform Convergence.- BIBLIOGRAPHY.- Index

About the Author

Enrique A. González-Velasco is a professor of mathematics at the University of Massachusetts at Lowell. His specialty is the history of math. He has also published a textbook on Fourier analysis and boundary value problems with a historical focus.

Reviews

From the reviews: "Describes the history of mathematics that gave rise to our modern concepts in calculus ... . Gonzalez-Velasco has done a marvelous job by sketching this very readable historical tale. ... not only compulsory reading for a course on the history of mathematics, but everyone teaching a calculus course should be aware of the roots and the wonderful achievements of the mathematical giants of the past centuries. They boldly went where nobody had gone before and paved the road for what we take for granted today." (A. Bultheel, The European Mathematical Society, March, 2012) "This detailed, carefully written volume is a selective history of mathematics, up to what might be considered the 'early modern period' ... with emphasis on 17th- and 18th-century advances. ... the book particularly suitable for undergraduate mathematics students, including those planning to teach in secondary schools. The volume contains an extensive bibliography with many original sources ... . A worthwhile addition to the literature. Summing Up: Highly recommended. Upper-division undergraduates through researchers/faculty." (S. J. Colley, Choice, Vol. 49 (7), March, 2012)