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Analysis I: Convergence, Elementary functions (Universitext) [Paperback]

Roger Godement , P. Spain
4.0 out of 5 stars  See all reviews (1 customer review)

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Book Description

November 18, 2003 3540059237 978-3540059233 Softcover reprint of the original 1st ed. 2004

Functions in R and C, including the theory of Fourier series, Fourier integrals and part of that of holomorphic functions, form the focal topic of these two volumes. Based on a course given by the author to large audiences at Paris VII University for many years, the exposition proceeds somewhat nonlinearly, blending rigorous mathematics skilfully with didactical and historical considerations. It sets out to illustrate the variety of possible approaches to the main results, in order to initiate the reader to methods, the underlying reasoning, and fundamental ideas. It is suitable for both teaching and self-study. In his familiar, personal style, the author emphasizes ideas over calculations and, avoiding the condensed style frequently found in textbooks, explains these ideas without parsimony of words. The French edition in four volumes, published from 1998, has met with resounding success: the first two volumes are now available in English.


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Analysis I: Convergence, Elementary functions (Universitext) + Analysis II: Differential and Integral Calculus, Fourier Series, Holomorphic Functions (Universitext)
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Editorial Reviews

Review

From the reviews of the original French edition:

"... The content is quite classical ... [...] The treatment is less classical: precise although unpedantic (rather far from the definition-theorem-corollary-style), it contains many interesting commentaries of epistemological, pedagogical, historical and even political nature. [...] The author gives frequent interesting hints on recent developments of mathematics connected to the concepts which are introduced. The Introduction also contains comments that are very unusual in a book on mathematical analysis, going from pedagogy to critique of the French scientific-military-industrial complex, but the sequence of ideas is introduced in such a way that readers are less surprised than they might be.
J. Mawhin in Zentralblatt Mathematik (1999)

From the reviews:

"Analysis I is the translation of the first volume of Godement’s four-volume work Analyse Mathématique, which offers a development of analysis more or less from the beginning up to some rather advanced topics. … the organization of the material is radically different … . It would … make excellent supplementary reading for honors calculus courses." (Gerald B. Folland, SIAM Review, Vol. 47 (3), 2005)

"A book on analysis that is quite different from all other books on this subject. … for those who essentially know the material (the level of an average graduate student, say), and who are interested in mathematics will certainly love reading it. Those who lecture this material may find a lot of inspiration to make their lessons entertaining." (Adhemar Bultheel, Bulletin of the Belgian Mathematical Society, Vol. 12 (2), 2005)

"Analysis I is an English translation of the first volume of a four-volume work. Analysis I consists of a spirally organized, organic, non-linear treatment of the introductory areas of ‘mathematical analysis as it was and as it has become’. It is infused with some excellent, sensitive appreciations of the work of pioneers … and reads as a heady blend of both classical concerns and modern refinements, often illuminated by a variety of approaches." (Nick Lord, The Mathematical Gazette, March, 2005)


Product Details

  • Series: Universitext
  • Paperback: 430 pages
  • Publisher: Springer; Softcover reprint of the original 1st ed. 2004 edition (November 18, 2003)
  • Language: English
  • ISBN-10: 3540059237
  • ISBN-13: 978-3540059233
  • Product Dimensions: 1 x 6 x 9.1 inches
  • Shipping Weight: 1.5 pounds (View shipping rates and policies)
  • Average Customer Review: 4.0 out of 5 stars  See all reviews (1 customer review)
  • Amazon Best Sellers Rank: #2,693,022 in Books (See Top 100 in Books)

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10 of 10 people found the following review helpful
4.0 out of 5 stars bbk_review December 14, 2010
Format:Paperback|Verified Purchase
Godement is a noted French mathematician who "personalizes" his approach to mathematical analysis. In both Volumes I & II the formal expository style so common to mathematical texts containing advanced material is for the most part absent. Generally the author organizes his discussions in a section around a related group of ideas and mathematical structures, such as an introduction to set theory, and attempts to give a self-contained account of the topics he chooses to cover. The style is informal, but the author does address key points in depth and with enough rigour that the reader who expects to grasp the material will have to be comfortable with mathematics as taught in a 2nd year honors course or 3rd year course of analysis taken by a math or science major at the undergraduate collegiate level. The author will often introduce historical asides or personal views which generally are an entertaining complement to the material under discussion. At its best the author's approach results in inspiring and insightful reading, while at its worst it can seem disjointed and rambling. Fortunately, the positives far outweigh the negatives in most sections. "Entertaining" is not generally used to describe mathematical exposition on topics at this level, but Godement's idiosyncractic style makes it seem appropriate. Volume I covers a variety of topics that would be included in the typical "Introductory Real Analysis" course while Volume II covers a variety of more advanced mathematical analysis topics that would be covered in courses like "Complex Analysis" or "Theory of Integration". Unfortunately, the other two volumes in this series of books have never been translated into English from their original French versions(Godement is a Professor of Mathematics at the University of Paris). Read more ›
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