LEADER 00000nam a2200457 i 4500 
001    978-3-319-52956-1 
003    DE-He213 
005    20170407153358.0 
006    m     o  d         
007    cr nn 008maaau 
008    170407s2017    gw      s         0 eng d 
020    9783319529561|q(electronic bk.) 
020    9783319529554|q(paper) 
024 7  10.1007/978-3-319-52956-1|2doi 
040    GP|cGP|erda|dAS 
041 0  eng 
050  4 QA303.2 
082 04 515.33|223 
100 1  Smorynski, Craig,|eauthor 
245 10 MVT :|ba most valuable theorem /|cby Craig Smorynski 
246 3  Mean Value Theorem 
264  1 Cham :|bSpringer International Publishing :|bImprint: 
300    1 online resource (x, 499 pages) :|billustrations, digital
       ;|c24 cm 
336    text|btxt|2rdacontent 
337    computer|bc|2rdamedia 
338    online resource|bcr|2rdacarrier 
347    text file|bPDF|2rda 
505 0  Introduction -- Curves and Tangents -- The Mean Value 
       Theorem -- Calculus Reform 
520    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 
650  0 Mean value theorems (Calculus) 
650 14 Mathematics 
650 24 Real Functions 
650 24 History of Mathematical Sciences 
710 2  SpringerLink (Online service) 
773 0  |tSpringer eBooks 
856 40 |uhttp://dx.doi.org/10.1007/978-3-319-52956-1