Calculus and its origins - David Perkins

Calculus and Its Origins is an overview of calculus as an intellectual pursuit having a 2,000-year history. Author David Perkins examines the extent to which mathematicians and scholars from Egypt, Persia, and India absorbed and nourished Greek geometry, and details how the scholars wove their inquiries into a unified theory. Chapters cover the story of Archimedes discovery of the area of a parabolic segment; ibn Al-Haytham s calculation of the volume of a revolved area; Jyesthadeva s explanation of the infinite series for sine and cosine; Wallis s deduction of the link between hyperbolas and logarithms; Newton s generalization of the binomial theorem; Leibniz s discovery of integration by parts-and much more. Each chapter also contains exercises by such mathematical luminaries as Pascal, Maclaurin, Barrow, Cauchy, and Euler.

Requiring only a basic knowledge of geometry and algebra-similar triangles, polynomials, factoring-and a willingness to treat the infinite as metaphor-Calculus and Its Origins is a treasure of the human intellect, pearls strung together by mathematicians across cultures and centuries.