Calculus and Its Origins (Spectrum)

Calculus and Its Origins is primarily a collection of results that show how calculus came to be, beginning in ancient Greece and climaxing with the discovery of calculus. Other books have traveled these paths, but they presuppose knowledge of calculus. This book requires only a basic knowledge of high school geometry and algebra. Exercises introduce further historical figures and their results, and make it possible for a professor to use this book in class. 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. ... Is Primarily A Collection Of Results That Show How Calculus Came To Be, Beginning In Ancient Greece And Climaxing With The Discovery Of Calculus. The Book Requires Only A Basic Knowledge Of High School Geometry And Algebra. Exercises Introduce Further Historical Figures And Their Results.--cover, P.[4]. The Ancients -- East Of Greece -- Motion -- Indivisibles -- Quadrature -- The Fundamental Theorem Of Calculus -- Notation -- Chords -- Zero Over Zero -- Rigor. David Perkins. Includes Bibliographical References (p. 153-160) And Index. ". . . Is primarily a collection of results that show how calculus came to be, beginning in ancient Greece and climaxing with the discovery of calculus. The book requires only a basic knowledge of high school geometry and algebra. Exercises introduce further historical figures and their results."--Page 4 of cover This book tells the story of how calculus came to be. It is accessible to anyone with a basic knowledge of geometry and algebra: pre-existing knowledge of calculus is not required. Exercises are included, which makes it ideal for use in the classroom.