Vector Analysis
Klaus Janich
ISBN:
9780387986494
Format:
Hardback
Publisher:
SpringerVerlag New York Inc.
Write a review
Printable
Presents modern vector analysis, and describes the classical notation and understanding of the theory. This book covers the classical vector analysis in Euclidean space, as well as on manifolds, and introduces de Rham Cohomology, Hodge theory, elementary differential geometry, and basic duality.
This book presents modern vector analysis and carefully describes the classical notation and understanding of the theory. It covers all of the classical vector analysis in Euclidean space, as well as on manifolds, and goes on to introduce de Rham Cohomology, Hodge theory, elementary differential geometry, and basic duality. The material is accessible to readers and students with only calculus and linear algebra as prerequisites. A large number of illustrations, exercises, and tests with answers make this book an invaluable selfstudy source.
ISBN  9780387986494   Weight (grammes)  745  ISBN13  9780387986494 (What's this?)   Language  German  Publisher  SpringerVerlag New York Inc.   Published in  New York, NY  Imprint  SpringerVerlag New York Inc.   Published in  US  Format  Hardback   Series title  Undergraduate Texts in Mathematics  Publication date  01 Feb 2001   Height (mm)  254  DEWEY  515.63   Width (mm)  178  DEWEY edition  DC21   Spine width (mm)  17  Pages  298  

 
  Preface to the English Edition      Preface to the First German Edition    1   Differentiable Manifolds   1  1.1   The Concept of a Manifold   1  1.2   Differentiable Maps   3  1.3   The Rank   5  1.4   Submanifolds   7  1.5   Examples of Manifolds   9  1.6   Sums, Products, and Quotients of Manifolds   12  1.7   Will Submanifolds of Euclidean Spaces Do?   17  2   The Tangent Space   25  2.1   Tangent Spaces in Euclidean Space   25  2.2   Three Versions of the Concept of a Tangent Space   27  2.3   Equivalence of the Three Versions   32  2.4   Definition of the Tangent Space   36  2.5   The Differential   37  2.6   The Tangent Spaces to a Vector Space   40  2.7   Velocity Vectors of Curves   41  2.8   Another Look at the Ricci Calculus   42  3   Differential Forms   49  3.1   Alternating [kappa]Forms   49  3.2   The Components of an Alternating [kappa]Form   51  3.3   Alternating nForms and the Determinant   54  3.4   Differential Forms   55  3.5   OneForms   57  4   The Concept of Orientation   65  4.1   Introduction   65    More...   
From the reviews: "The present book is a marvelous introduction in the modern theory of manifolds and differential forms. The undergraduate student can closely examine tangent spaces, basic concepts of differential forms, integration on manifolds, Stokes theorem, de Rhamcohomology theorem, differential forms on Riemannian manifolds, elements of the theory of differential equations on manifolds (LaplaceBeltrami operators). Every chapter contains useful exercises for the students."'ZENTRALBLATT MATH "Within the ambit of the MMath there is increasing need for good source material for reading courses in the 4th year. This is just such a source. It is extremely well written. The exercises are well thought out and, for instance, each chapter ends with a section that discusses rather than solves the exercises. It is very user friendly ... . The book is quite well priced and is one to consider seriously for library purchase. ... I enjoyed working my way through it immensely." (Tim Porter, The Mathematical Gazette, Vol. 86 (506), 2002) "'Vector analysis' or 'vector calculus,' as it is sometimes known, is one of the most fascinating subjects in the undergraduate mathematics curriculum. It also is one of the subjects that has the largest number of dramatically different incarnations. ... Klaus Janich's Vector Analysis is about differential manifolds, differential forms, and integration on manifolds. The approach is quite sophisticated, but the author does try to be more helpful to readers than the typical advanced mathematics text." (MAA online, Mathematical Association of America, November, 2004) "This is a text on calculus on manifolds ... for readers who know only the calculus of several variables ... . each chapter contains tests and exercises. The exercises are well selected and enhance the description of the text, but one of the special features of this book is the tests. They are in marksheet style. Each problem is easy but appropriate to test the understanding of the reader, so this makes the book suitable for anyone studying the subject independently." (Akira Asada, Mathematical Reviews, Issue 2001 m) "This book is very easily accessible and self contained, clearly recalling at various points the facts from linear algebra which are needed in the progress. This does not mean, though, that we are dealing with a lowaiming text, on the contrary: a big effort is made to let the reader catch a glimpse of the way mathematical results are achieved. ... Moreover, the author constantly tries to make the less vigilant reader aware of possible subtle difficulties or not completely straightforward conclusions." (F. Pasquotto, Nieuw Archief voor Wiskunde, Vol. 4 (3), 2003) "When and how to introduce students to surface integration ... is difficult to answer. ... This book offers a very nice description of the basic conceptual tools needed to explain these topics to mathematics students ... . A nice feature is that it contains many figures (making easier an intuitive understanding of the treated topics), exercises with hints, and tests with answers. ... It is certainly one of the best books in the field and can be strongly recommended for a general mathematical audience." (European Mathematical Society Newsletter, June, 2002) "The author ties together different approaches to the tangent space of a manifold coming from germs of realvalued functions, smooth curves, and that commonly adopted in physics literature based on Ricci calculus. This enables the reader to move between sources with little difficulty. Each chapter contains a test consisting of multiplechoice questions. The answers are provided and the reader is warned that some of the questions are so obviously simple that a healthy scare will result when they prove not to be so." (Nigel Steele, Times Higher Education Supplement, November, 2002) "This essentially modern text carefully develops vector analysis on manifolds, reinterprets it from the classical viewpoint (and with the classical notation) for threedimensional Euclidean space, and then goes on to introduce de Rham cohomology and Hodge theory. The material is accessible to an undergraduate student with calculus, linear algebra, and some topology as prerequisites." (L'Enseignement Mathematique, Vol. 47 (12), 2001) Be the first to write a customer review


£51.16
Dispatched within 48 hours
Reserve instore:
Not currently stocked in Blackwell shops.
Ask your local shop to obtain this title for you.
Find at
Google Books:
