000 03712nam a22004575i 4500
001 978-0-8176-8304-7
003 DE-He213
005 20140220083227.0
007 cr nn 008mamaa
008 111103s2012 xxu| s |||| 0|eng d
020 _a9780817683047
_9978-0-8176-8304-7
024 7 _a10.1007/978-0-8176-8304-7
_2doi
050 4 _aQA641-670
072 7 _aPBMP
_2bicssc
072 7 _aMAT012030
_2bisacsh
082 0 4 _a516.36
_223
100 1 _aBachman, David.
_eauthor.
245 1 2 _aA Geometric Approach to Differential Forms
_h[electronic resource] /
_cby David Bachman.
250 _aSecond.
264 1 _aBoston :
_bBirkhäuser Boston,
_c2012.
300 _aXVI, 156p. 43 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
505 0 _aPreface -- Guide to the Reader.-Multivariable Calculus -- Parameterizations -- Introduction to Forms -- Forms -- Differential Forms -- Differentiation of Forms -- Stokes' Theorem -- Applications -- Manifolds -- Non-linear Forms -- References -- Index -- Solutions.
520 _a"[The author's] idea is to use geometric intuition to alleviate some of the algebraic difficulties...The emphasis is on understanding rather than on detailed derivations and proofs. This is definitely the right approach in a course at this level."   —MAA Reviews (Review of First Edition) "The book certainly has its merits and is very nicely illustrated … . It should be noted that the material, which has been tested already in the classroom, aims at three potential course tracks: a course in multivariable calculus, a course in vector calculus and a course for more advanced undergraduates (and beginning graduates)."                                                                                   —Mathematical Reviews (Review of First Edition) The modern subject of differential forms subsumes classical vector calculus. This text presents differential forms from a geometric perspective accessible at the advanced undergraduate level.  The author approaches the subject with the idea that complex concepts can be built up by analogy from simpler cases, which, being inherently geometric, often can be best understood visually. Each new concept is presented with a natural picture that students can easily grasp; algebraic properties then follow. This facilitates the development of differential forms without assuming a background in linear algebra. Throughout the text, emphasis is placed on applications in 3 dimensions, but all definitions are given so as to be easily generalized to higher dimensions. The second edition includes a completely new chapter on differential geometry, as well as other new sections, new exercises and new examples. Additional solutions to selected exercises have also been included. The work is suitable for use as the primary textbook for a sophomore-level class in vector calculus, as well as for more upper-level courses in differential topology and differential geometry.
650 0 _aMathematics.
650 0 _aGlobal analysis.
650 0 _aGlobal differential geometry.
650 1 4 _aMathematics.
650 2 4 _aDifferential Geometry.
650 2 4 _aGlobal Analysis and Analysis on Manifolds.
650 2 4 _aReal Functions.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9780817683030
856 4 0 _uhttp://dx.doi.org/10.1007/978-0-8176-8304-7
912 _aZDB-2-SMA
999 _c100238
_d100238