000			04527nam a2200769 i 4500
001			7056255
003			IEEE
005			20200413152917.0
006			m eo d
007			cr cn |||m|||a
008			150320s2015 caua foab 001 0 eng d
020			_a9781627056632 _qebook
020			_z9781627056625 _qprint
024	7		_a10.2200/S00632ED1V01Y201502MAS015 _2doi
035			_a(CaBNVSL)swl00404796
035			_a(OCoLC)905421782
040			_aCaBNVSL _beng _erda _cCaBNVSL _dCaBNVSL
050		4	_aQA641 _b.G552 2015
082	0	4	_a516.36 _223
100	1		_aGilkey, Peter B., _eauthor.
245	1	0	_aAspects of differential geometry I / _cPeter Gilkey, JeongHyeong Park, Ramón Vázquez-Lorenzo.
264		1	_aSan Rafael, California (1537 Fourth Street, San Rafael, CA 94901 USA) : _bMorgan & Claypool, _c2015.
300			_a1 PDF (xiii, 140 pages) : _billustrations.
336			_atext _2rdacontent
337			_aelectronic _2isbdmedia
338			_aonline resource _2rdacarrier
490	1		_aSynthesis lectures on mathematics and statistics, _x1938-1751 ; _v# 15
538			_aMode of access: World Wide Web.
538			_aSystem requirements: Adobe Acrobat Reader.
500			_aPart of: Synthesis digital library of engineering and computer science.
504			_aIncludes bibliographical references (pages 131-133) and index.
505	0		_a1. Basic notions and concepts -- 1.1 Metric spaces -- 1.2 Linear algebra -- 1.3 The derivative -- 1.4 The inverse and implicit function theorems -- 1.5 The Riemann integral -- 1.6 Improper integrals -- 1.7 The change of variable theorem --
505	8		_a2. Manifolds -- 2.1 Smooth manifolds -- 2.2 The tangent and cotangent bundles -- 2.3 Stokes' theorem -- 2.4 Applications of stokes' theorem --
505	8		_a3. Riemannian and pseudo-Riemannian geometry -- 3.1 The pseudo-Riemannian measure -- 3.2 Connections -- 3.3 The Levi-Civita connection -- 3.4 Geodesics -- 3.5 The Jacobi operator -- 3.6 The Gauss-Bonnet theorem -- 3.7 The Chern-Gauss-Bonnet theorem --
505	8		_aBibliography -- Authors' biographies -- Index.
506	1		_aAbstract freely available; full-text restricted to subscribers or individual document purchasers.
510	0		_aCompendex
510	0		_aINSPEC
510	0		_aGoogle scholar
510	0		_aGoogle book search
520	3		_aDifferential Geometry is a wide field. We have chosen to concentrate upon certain aspects that are appropriate for an introduction to the subject; we have not attempted an encyclopedic treatment. In Book I, we focus on preliminaries. Chapter 1 provides an introduction to multivariable calculus and treats the Inverse Function Theorem, Implicit Function Theorem, the theory of the Riemann Integral, and the Change of Variable Theorem. Chapter 2 treats smooth manifolds, the tangent and cotangent bundles, and Stokes' Theorem. Chapter 3 is an introduction to Riemannian geometry. The Levi-Civita connection is presented, geodesics introduced, the Jacobi operator is discussed, and the Gauss-Bonnet Theorem is proved. The material is appropriate for an undergraduate course in the subject. We have given some different proofs than those that are classically given and there is some new material in these volumes. For example, the treatment of the Chern-Gauss-Bonnet Theorem for pseudo-Riemannian manifolds with boundary is new.
530			_aAlso available in print.
588			_aTitle from PDF title page (viewed on March 20, 2015).
650		0	_aGeometry, Differential.
653			_aChange of Variable Theorem
653			_aderivative as best linear approximation
653			_aFubini's Theorem
653			_aGauss-Bonnet Theorem
653			_aGauss's Theorem
653			_ageodesic
653			_aGreen's Theorem
653			_aImplicit Function Theorem
653			_aimproper integrals
653			_aInverse Function Theorem
653			_aLevi-Civita connection
653			_apartitions of unity
653			_apseudo-Riemannian geometry
653			_aRiemann integral
653			_aRiemannian geometry
653			_aStokes' Theorem
700	1		_aPark, JeongHyeong., _eauthor.
700	1		_aVázquez-Lorenzo, Ramón., _eauthor.
776	0	8	_iPrint version: _z9781627056625
830		0	_aSynthesis digital library of engineering and computer science.
830		0	_aSynthesis lectures on mathematics and statistics ; _v# 15. _x1938-1751
856	4	2	_3Abstract with links to resource _uhttp://ieeexplore.ieee.org/servlet/opac?bknumber=7056255
999			_c562122 _d562122