1976

Enrique A. Gonzlez-Velasco.

Springer

2011

xi, 466 p. ill. 24 cm

Includes bibliographical references and index , 1. TRIGONOMETRY. The Hellenic period -- Ptolemy's table of chords -- The Indian contribution -- Trigonometry in the Islamic World -- Trigonometry in Europe -- From Vite to Pitiscus -- 2. LOGARITHMS. Napier's first three tables -- Napier's logarithms -- Briggs' logarithms -- Hyperbolic logarithms -- Newton's binomial series -- The logarithm according to Euler -- 3. COMPLEX NUMBERS. The depressed cubic -- Cardano's contribution -- The birth of complex numbers -- Higher-order roots of complex numbers -- The logarithms of complex numbers -- Caspar Wessel's breakthrough -- Gauss and Hamilton have the final word -- 4. INFINITE SERIES. The origins -- The summation of series -- The expansion of functions -- The Taylor and Maclaurin series -- 5. THE CALCULUS. The origins -- Fermat's method of maxima and minima -- Fermat's treatise on quadratures -- Gregory's contributions -- Barrow's geometric calculus -- From tangents to quadratures -- Newton's method of infinite series -- Newton's method of fluxions -- Was Newton's tangent method original? -- Newton's first and last ratios -- Newton's last version of the calculus -- Leibniz' calculus : 1673-1675 -- Leibniz' calculus : 1676-1680 -- The arithmetical quadrature -- Leibniz' publications -- The aftermath -- 6. CONVERGENCE. To the limit -- The vibrating string makes waves -- Fourier puts on the heat -- The convergence of series --The difference quotient -- The derivative -- Cauchy's integral calculus -- Uniform convergence.

QA

21

.G66

2011