Mvt: A Most Valuable Theorem

ISBN-13: 9783319529554 / Angielski / Miękka / 2017 / 499 str.

Craig Smorynski

Opis

This book is about the rise and supposed fall of the mean value theorem. It discusses the evolution of the theorem and the concepts behind it, how the theorem relates to other fundamental results in calculus, and modern re-evaluations of its role in the standard calculus course. The mean value theorem is one of the central results of calculus. It was called -the fundamental theorem of the differential calculus- because of its power to provide simple and rigorous proofs of basic results encountered in a first-year course in calculus. In mathematical terms, the book is a thorough treatment of this theorem and some related results in the field; in historical terms, it is not a history of calculus or mathematics, but a case study in both. MVT: A Most Valuable Theorem is aimed at those who teach calculus, especially those setting out to do so for the first time. It is also accessible to anyone who has finished the first semester of the standard course in the subject and will be of interest to undergraduate mathematics majors as well as graduate students. Unlike other books, the present monograph treats the mathematical and historical aspects in equal measure, providing detailed and rigorous proofs of the mathematical results and even including original source material presenting the flavour of the history.

Recenzje

"The book under review is written as a hybrid between a mathematical textbook and a history of mathematics concerning the Mean Value Theorem, with strong accents on the historical aspects. ... This is an unusual but interesting textbook. ... The book will be of interest to undergraduate mathematics majors, graduate students and those who are teaching calculus. Also, it is recommended to everyone interested in the history of mathematics." (Sarin Gheorghe Gal, Mathematical Reviews, November, 2017)

"The Mean Value Theorem is a key result in elementary calculus, taught in every first-year calculus class. ... this book is an interesting read for all mathematicians; it contains little known nuggets of information which could be useful for teachers to attract the interest of their students." (Phill Schultz, Gazette of the Australian Mathematical Society, Vol. 44 (5), November, 2017)

"This excellent source book on the MVT will provide a wide mathematical audience with insight into its history, proof, and place in mathematical pedagogy. ... This book will be an excellent choice for a capstone course for mathematics majors, an invaluable reference for any individual teaching calculus, or simply an enjoyable read for one who has completed calculus and wants to delve more deeply into the MVT and its history. Summing Up: Recommended. Upper-division undergraduates and above; faculty and professionals." (R. L. Pour, Choice, Vol. 55 (2), October, 2017)

"The book under review discusses the evolution of the mean-value theorem and of some of the concepts behind it. ... the present volume is concerned with some mathematical and historical aspects related with the mean-value theorem. The author provides detailed and rigorous proofs of the mathematical results and even includes original source material presenting the flavour of the history." (Teodora Liliana Radulescu, zbMATH, 1372.26002, 2017)

Spis treści

Introduction.- Curves and Tangents.- The Mean Value Theorem.- Calculus Reform.