Calculus and Its Origins

David Perkins teaches mathematics at Luzerne County Community College. He earned his doctorate from the University of Montana in 1995.

Perkins (Luzerne County Community College) provides an interesting look at the historic development of selected calculus topics. This is not a textbook in the traditional sense but a supplement to fill in details across the 2,000-year history of the subject. The work is divided into ten chapters beginning with ""The Ancients"" and ""East of Greece."" Later chapters discuss the contributions of Fermat, Newton, Leibniz, Lagrange, Cauchy, and more. The exercises are not routine practice problems, but rather more thoughtful, involved problems that build on the material introduced. The book may work well as a complement to a history of math course; it might also be useful for an independent study for advanced students. Because of the connection presented, students should have at least one semester of calculus before reading it. For the professor, the book offers much material to bring into a traditional calculus course to give students a historical perspective on the subject and some ideas for possible writing assignments/explorations for students to complete outside of class. Overall, a good source to bring history to calculus and to actively engage students in the development of the discipline."" - Choice""Differential and integral calculus is a subject that you can learn in a few courses, but it often takes many more years before it is truly appreciated. The enormous breadth of the subjects where it is used can astound even veterans of the practice of the art. Recently I was tutoring a student in AP calculus and we were discussing the derivative as a rate of change. I told her that since all things in the world change over time, the derivative describes everything. It may have been a bit of hyperbole, but at most only a bit. This book traces the mathematical and historical roots of calculus and it quite rightly begins with a couple of forms of Zeno's paradox. As is nearly always the case something is labeled as a paradox when it is not completely understood and that is the case with Zeno's famous puzzle. The fundamentals of limits and calculus explain the solution to Zeno's paradox quite well, but it took centuries of incremental advancement and the work of several geniuses to get there.That work is summarized in a very succinct and effective manner by Perkins; he walks through the major discoveries that moved the level of understanding progressively upward. The explanations are very well done, with suitable instructor help; they can be understood by anyone that has gone through the complete high school course sequence in algebra and geometry. This book could also be used in a course in the history of mathematics; exercises that take the students in directions that extend the material are included at the end of the chapters. Solutions are not included because they are to be in essay form and generally require some research. They are very good and are challenging enough so that any subset could serve as the basis of a complete grade.No matter what level of mathematics you reach or area you work in, there are books that will always be worthy of reading. This is one of them."" - Charles Ashbacher, Journal of Recreational Mathematics""The goal of this book is to ""teach calculus as the culmination of an intellectual pursuit and place the discovery of calculus at the end."" The author succeeds admirably in describing this pursuit and its culmination in such a short book. ...The book is a very good and original addition to the calculus literature. The prose is very agreeable. It looks very nice too: all figures are wonderful hand-drawn pictures. One wonders whether they could be brought to life in the classroom with some computer animation. ...The book concentrates on the mathematics, leaving the history in the background, except that the main actors are mentioned. This is not a treatise on the discovery or invention of calculus. ... What the book does provide is good side reading for both students and instructors. If the instructor can deliver in the classroom what the book contains, it'll be a success for its freshness and intrinsic interest. In any case, reading the book is a pleasure, and the exercises are unusual and can be challenging. I've enjoyed reading it and I'm certain you will too."" - Luiz Henrique de Figueiredo, MAA Reviews

• Preface; 1. The Ancients; 2. East of Greece; 3. Motion; 4. Indivisibles; 5. Quadrature; 6. The Fundamental Theorem of Calculus; 7. Notation; 8. Chords; 9. Zero over zero; 10. Rigor.