000			03344nam a22004695i 4500
001			978-1-4419-7332-0
003			DE-He213
005			20140220084511.0
007			cr nn 008mamaa
008			100917s2010 xxu| s |||| 0|eng d
020			_a9781441973320 _9978-1-4419-7332-0
024	7		_a10.1007/978-1-4419-7332-0 _2doi
050		4	_aQA299.6-433
072		7	_aPBK _2bicssc
072		7	_aMAT034000 _2bisacsh
082	0	4	_a515 _223
100	1		_aCallahan, James J. _eauthor.
245	1	0	_aAdvanced Calculus _h[electronic resource] : _bA Geometric View / _cby James J. Callahan.
264		1	_aNew York, NY : _bSpringer New York, _c2010.
300			_aXVI, 526 p. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aUndergraduate Texts in Mathematics, _x0172-6056
505	0		_aStarting Points -- Geometry of Linear Maps -- Approximations -- The Derivative -- Inverses -- Implicit Functions -- Critical Points -- Double Integrals -- Evaluating Double Integrals -- Surface Integrals -- Stokes’ Theorem.
520			_aWith a fresh geometric approach that incorporates more than 250 illustrations, this textbook sets itself apart from all others in advanced calculus. Besides the classical capstones--the change of variables formula, implicit and inverse function theorems, the integral theorems of Gauss and Stokes--the text treats other important topics in differential analysis, such as Morse's lemma and the Poincaré lemma. The ideas behind most topics can be understood with just two or three variables. This invites geometric visualization; the book incorporates modern computational tools to give visualization real power. Using 2D and 3D graphics, the book offers new insights into fundamental elements of the calculus of differentiable maps, such as the role of the derivative as the local linear approximation to a map and its role in the change of variables formula for multiple integrals. The geometric theme continues with an analysis of the physical meaning of the divergence and the curl at a level of detail not found in other advanced calculus books. Advanced Calculus: A Geometric View is a textbook for undergraduates and graduate students in mathematics, the physical sciences, and economics. Prerequisites are an introduction to linear algebra and multivariable calculus. There is enough material for a year-long course on advanced calculus and for a variety of semester courses--including topics in geometry. It avoids duplicating the material of real analysis. The measured pace of the book, with its extensive examples and illustrations, make it especially suitable for independent study.
650		0	_aMathematics.
650		0	_aGlobal analysis (Mathematics).
650	1	4	_aMathematics.
650	2	4	_aAnalysis.
650	2	4	_aApplications of Mathematics.
650	2	4	_aReal Functions.
650	2	4	_aApproximations and Expansions.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9781441973313
830		0	_aUndergraduate Texts in Mathematics, _x0172-6056
856	4	0	_uhttp://dx.doi.org/10.1007/978-1-4419-7332-0
912			_aZDB-2-SMA
999			_c110740 _d110740