Journey through Mathematics

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