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Analysis by Its History (Undergraduate Texts in Mathematics) | 
 enlarge | Authors: Gerhard Wanner, Ernst Hairer
Publisher: Springer
Category: Book
List Price: $39.95
Buy New: $35.95
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Avg. Customer Rating:  8 reviews
Sales Rank: 637425
Media: Paperback
Edition: 1st ed. 1996. 2nd printing
Number Of Items: 1
Pages: 382
Shipping Weight (lbs): 1.2
Dimensions (in): 9.2 x 6.1 x 0.7
ISBN: 0387770313
Dewey Decimal Number: 515
EAN: 9780387770314
ASIN: 0387770313
Publication Date: June 2, 2008
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Product Description
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.
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| Customer Reviews: Read 3 more reviews...
 contains very good historical perspectives on analysis July 21, 2008
This very interesting book contains very good historical perspectives on analysis. If you want to know how things like trigonometric functions, logarithms, infinite series, differential and integral calculus and differential equations come about (but written from a modern viewpoint), then this is the book for you. It is not a book for casual reading like E T Bell's Men of Mathematics, but the reader will learn a lot of college and undergraduate mathematics along the way.
A quite magnificent book April 12, 2007
2 out of 3 found this review helpful
I return to this book again and again just out of sheer pleasure. The depth of scholarship of the authors shines through on every page and the choice of historical material is fascinating.Topics like compactness and uniform convergence can here be seen to have arisen out of genuine necessity-they are not (as would seem from other books)mere names in a standard syllabus. If you have any mathematica interest at all, take this book on holiday and sleep with it under the pillow to extract more from it by osmotic pressure overnight.
A Good Mix of Calculus and its History January 9, 2007
3 out of 3 found this review helpful
This books gives a unique approach to Calculus using its historical development. The most notable feature of the book is that the order of topics is reversed from what has become standard in current textbooks. It begins with the analysis of areas and volumes. This is followed by derivatives, continuity, and the notion of function. This is the order in which analysis developed, but not the order one would follow if building understanding of the subject from a foundation upward. Historically, the foundations were laid last.
The book is not intended as a history of analysis. It is rather intended as a textbook or reference in which the topics are presented in historical order. The historical background is intended to give insight into a modern view of the subject. It accomplishes this admirably.
The book is filled with examples, quotes, vignettes, historical background, computer graphics, and copies of original documents. Special topics are interspersed throughout. The book gives us a fresh and envigorating view of Calculus. It is an invaluable resource.
 A somewhat useful scrapbook with a poor second half April 7, 2006
3 out of 5 found this review helpful
Chapters 1 and 2 treat classical differential and integral calculus. This is a disorganised mess of historical and mathematical tidbits. It's not a great place to learn calculus, but it's good side reading since there are many interesting topics, some of which are often neglected in today's books: continued fractions (!), complex functions already on page 56, an interesting section on differential geometry, Euler-Maclaurin summation, etc. The authors also have the very commendable habit of including charming facsimiles of figures from original works.
Chapter 3 "Foundations of Classical Analysis" and chapter 4 "Calculus in Several Variables" are almost completely ahistorical. The "by its history" part of the exposition is restricted to some scattered superficial remarks, including silly nonsense such as that if Leibniz had know of the intricate progression of theorems needed for a modern proof of the "fundamental theorem" then "he might not have had the courage to state and use this theorem" (p. 239). And in another parodic misuse of the historical perspective, the authors introduce Descartes's folium merely for the purpose of practising the determination of stationary points (p. 322)---of course, Descartes introduced the folium for a much more interesting purpose, but to learn that story we must look for an "Analysis by Its History" book worthy of its name.
Brilliant, unorthodox, a very commendable approach. September 1, 2000
24 out of 25 found this review helpful
I wish there had been books like this when I was at (high)school! It is one of those rare books that bridge the yawning gap between the popular personalised history books that are so inspiring to the young mind, (eg. E.T.Bell's "Men of Mathematics", Kasner & Newman's "Mathematics & the Imagination" or Kak & Ulam's "Logic and(?) Mathematics") and the terse, somewhat desiccated university text books. This can leave the undergraduate not fully appreciating the motivation for exhaustive rigor and also losing any perspective of where the abstract theorems and lemmas are ultimately distilled from. This book links the historical characters, controversies and challenges with the modern techniques that gradually emerged to deal with the pathological behaviour of sets, series and functions. It would be a mistake to confuse this book, as some of your reviewers have done, with the many first-year undergraduate texts that are available. It could be regarded as a sophisticated high school book that gives a real flavour of how the classical problems are treated in modern rigorous style, or alternatively as a colourful motivational aid to early undergraduate analysis courses. I hope that the publishers encourage similar ventures in other branches of the subject, for instance algebra, differential & integral equations, probability and perhaps even quantum theory.
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