000 03448nam a22004695i 4500
001 978-0-8176-4520-5
003 DE-He213
005 20161121231030.0
007 cr nn 008mamaa
008 100301s2006 xxu| s |||| 0|eng d
020 _a9780817645205
_9978-0-8176-4520-5
024 7 _a10.1007/978-0-8176-4520-5
_2doi
050 4 _aQA614-614.97
072 7 _aPBKS
_2bicssc
072 7 _aMAT034000
_2bisacsh
082 0 4 _a514.74
_223
100 1 _aBachman, David.
_eauthor.
245 1 2 _aA Geometric Approach to Differential Forms
_h[electronic resource] /
_cby David Bachman.
264 1 _aBoston, MA :
_bBirkhäuser Boston,
_c2006.
300 _aXVI, 133 p. 39 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
505 0 _aMultivariable Calculus -- Parameterizations -- to Forms -- Forms -- Differential Forms -- Differentiation of Forms -- Stokes’ Theorem -- Applications -- Manifolds.
520 _aThe modern subject of differential forms subsumes classical vector calculus. This text presents differential forms from a geometric perspective accessible at the undergraduate level. The book begins with basic concepts such as partial differentiation and multiple integration and gently develops the entire machinery of differential forms. 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. A centerpiece of the text is the generalized Stokes' theorem. Although this theorem implies all of the classical integral theorems of vector calculus, it is far easier for students to both comprehend and remember. The text is designed to support three distinct course tracks: the first as the primary textbook for third semester (multivariable) calculus, suitable for anyone with a year of calculus; the second is aimed at students enrolled in vector calculus; while the third targets advanced undergraduates and beginning graduate students in physics or mathematics, touching on more advanced topics such as Maxwell's equations, foliation theory, and cohomology. Containing excellent motivation, numerous illustrations and solutions to selected problems in an appendix, the material has been tested in the classroom along all three potential course tracks.
650 0 _aMathematics.
650 0 _aGlobal analysis (Mathematics).
650 0 _aManifolds (Mathematics).
650 0 _aFunctions of real variables.
650 0 _aDifferential geometry.
650 1 4 _aMathematics.
650 2 4 _aGlobal Analysis and Analysis on Manifolds.
650 2 4 _aReal Functions.
650 2 4 _aDifferential Geometry.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9780817644994
856 4 0 _uhttp://dx.doi.org/10.1007/978-0-8176-4520-5
912 _aZDB-2-SMA
950 _aMathematics and Statistics (Springer-11649)
999 _c507539
_d507539