History Calculus

This textbook provides a unified and concise exploration of undergraduate mathematics by approaching the subject through its history. Readers will discover the rich tapestry of ideas behind familiar topics from the undergraduate curriculum, such as calculus, algebra, topology, and more. Featuring historical episodes ranging from the Ancient Greeks to Fermat and Descartes, this volume offers a glimpse into the broader context in which these ideas developed, revealing unexpected connections that make this ideal for a senior capstone course.

Develop a deep understanding and intuition for calculus. Solve problems and implement algorithms by hand and in Python.

This book presents first-year calculus roughly in the order in which it first was discovered. The first two chapters show how the ancient calculations of practical problems led to infinite series, differential and integral calculus and to differential equations. The establishment of mathematical rigour for these subjects in the 19th century for one and several variables is treated in chapters III and IV. The text is complemented by a large number of examples, calculations and mathematical pictures and will provide stimulating and enjoyable reading for students, teachers, as well as researchers.

Shortlisted for the Royal Society Science Book Prize 2019

Intended for a one- or two-semester course, this text applies basic, one-variable calculus to analyze the motion both of planets in their orbits as well as interplanetary spacecraft in their trajectories. The remarkable spacecraft missions to the inner and outermost reaches of our solar system have been one of the greatest success stories of modern human history. Much of the underlying mathematical story is presented alongside the astonishing images and extensive data that NASA’s Voyager, NEAR-Shoemaker, Cassini, and Juno missions have sent back to us.