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.
