000			04322nam a22004815i 4500
001			978-3-540-28890-9
003			DE-He213
005			20161121230934.0
007			cr nn 008mamaa
008			100301s2005 gw | s |||| 0|eng d
020			_a9783540288909 _9978-3-540-28890-9
024	7		_a10.1007/3-540-28890-2 _2doi
050		4	_aQA299.6-433
072		7	_aPBK _2bicssc
072		7	_aMAT034000 _2bisacsh
082	0	4	_a515 _223
100	1		_aJost, Jürgen. _eauthor.
245	1	0	_aPostmodern Analysis _h[electronic resource] / _cby Jürgen Jost.
250			_aThird Edition.
264		1	_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg, _c2005.
300			_aXV, 375 p. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aUniversitext
505	0		_aCalculus for Functions of One Variable -- Prerequisites -- Limits and Continuity of Functions -- Differentiability -- Characteristic Properties of Differentiable Functions. Differential Equations -- The Banach Fixed Point Theorem. The Concept of Banach Space -- Uniform Convergence. Interchangeability of Limiting Processes. Examples of Banach Spaces. The Theorem of Arzela-Ascoli -- Integrals and Ordinary Differential Equations -- Topological Concepts -- Metric Spaces: Continuity, Topological Notions, Compact Sets -- Calculus in Euclidean and Banach Spaces -- Differentiation in Banach Spaces -- Differential Calculus in $$\mathbb{R}$$ d -- The Implicit Function Theorem. Applications -- Curves in $$\mathbb{R}$$ d. Systems of ODEs -- The Lebesgue Integral -- Preparations. Semicontinuous Functions -- The Lebesgue Integral for Semicontinuous Functions. The Volume of Compact Sets -- Lebesgue Integrable Functions and Sets -- Null Functions and Null Sets. The Theorem of Fubini -- The Convergence Theorems of Lebesgue Integration Theory -- Measurable Functions and Sets. Jensen’s Inequality. The Theorem of Egorov -- The Transformation Formula -- and Sobolev Spaces -- The Lp-Spaces -- Integration by Parts. Weak Derivatives. Sobolev Spaces -- to the Calculus of Variations and Elliptic Partial Differential Equations -- Hilbert Spaces. Weak Convergence -- Variational Principles and Partial Differential Equations -- Regularity of Weak Solutions -- The Maximum Principle -- The Eigenvalue Problem for the Laplace Operator.
520			_aWhat is the title of this book intended to signify, what connotations is the adjective “Postmodern” meant to carry? A potential reader will surely pose this question. To answer it, I should describe what distinguishes the - proach to analysis presented here from what has by its protagonists been called “Modern Analysis”. “Modern Analysis” as represented in the works of the Bourbaki group or in the textbooks by Jean Dieudonn´ e is characterized by its systematic and axiomatic treatment and by its drive towards a high level of abstraction. Given the tendency of many prior treatises on analysis to degenerate into a collection of rather unconnected tricks to solve special problems, this de?nitely represented a healthy achievement. In any case, for the development of a consistent and powerful mathematical theory, it seems to be necessary to concentrate solely on the internal problems and structures and to neglect the relations to other ?elds of scienti?c, even of mathematical study for a certain while. Almost complete isolation may be required to reach the level of intellectual elegance and perfection that only a good mathem- ical theory can acquire. However, once this level has been reached, it can be useful to open one’s eyes again to the inspiration coming from concrete external problems.
650		0	_aMathematics.
650		0	_aMathematical analysis.
650		0	_aAnalysis (Mathematics).
650		0	_aPartial differential equations.
650	1	4	_aMathematics.
650	2	4	_aAnalysis.
650	2	4	_aPartial Differential Equations.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9783540258308
830		0	_aUniversitext
856	4	0	_uhttp://dx.doi.org/10.1007/3-540-28890-2
912			_aZDB-2-SMA
950			_aMathematics and Statistics (Springer-11649)
999			_c506168 _d506168