000			03493nam a22005295i 4500
001			978-3-0348-0636-7
003			DE-He213
005			20140220082836.0
007			cr nn 008mamaa
008			130725s2013 sz | s |||| 0|eng d
020			_a9783034806367 _9978-3-0348-0636-7
024	7		_a10.1007/978-3-0348-0636-7 _2doi
050		4	_aQA331.5
072		7	_aPBKB _2bicssc
072		7	_aMAT034000 _2bisacsh
072		7	_aMAT037000 _2bisacsh
082	0	4	_a515.8 _223
100	1		_aKriz, Igor. _eauthor.
245	1	0	_aIntroduction to Mathematical Analysis _h[electronic resource] / _cby Igor Kriz, Aleš Pultr.
264		1	_aBasel : _bSpringer Basel : _bImprint: Birkhäuser, _c2013.
300			_aXX, 510 p. 1 illus. in color. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
505	0		_aPreface -- Introduction -- Part 1. A Rigorous Approach to Advanced Calculus -- 1. Preliminaries -- 2. Metric and Topological Spaces I -- 3. Multivariable Differential Calculus -- 4. Integration I: Multivariable Riemann Integral and Basic Ideas toward the Lebesgue Integral -- 5. Integration II: Measurable Functions, Measure and the Techniques of Lebesgue Integration -- 6. Systems of Ordinary Differential Equations -- 7. System of Linear Differential Equations -- 8. Line Integrals and Green's Theorem -- Part 2. Analysis and Geometry -- 9. An Introduction to Complex Analysis -- 10. Metric and Topological Spaces II -- 11. Multilinear Algebra -- 12. Smooth Manifolds, Differential Forms and Stokes' Theorem -- 13. Calculus of Variations and the Geodesic Equation -- 14. Tensor Calculus and Riemannian Geometry -- 15. Hilbert Spaces I: Definitions and Basic Properties -- 16. Hilbert Spaces II: Examples and Applications -- Appendix A. Linear Algebra I: Vector Spaces -- Appendix B. Linear Algebra II: More about Matrices -- Bibliography -- Index of Symbols -- Index.  .
520			_aThe book begins at an undergraduate student level, assuming only basic knowledge of calculus in one variable. It rigorously treats topics such as multivariable differential calculus, the Lebesgue integral, vector calculus and differential equations. After having created a solid foundation of topology and linear algebra, the text later expands into more advanced topics such as complex analysis, differential forms, calculus of variations, differential geometry and even functional analysis. Overall, this text provides a unique and well-rounded introduction to the highly developed and multi-faceted subject of mathematical analysis as understood by mathematicians today.
650		0	_aMathematics.
650		0	_aMatrix theory.
650		0	_aFunctions of complex variables.
650		0	_aDifferential Equations.
650		0	_aSequences (Mathematics).
650	1	4	_aMathematics.
650	2	4	_aReal Functions.
650	2	4	_aLinear and Multilinear Algebras, Matrix Theory.
650	2	4	_aMeasure and Integration.
650	2	4	_aFunctions of a Complex Variable.
650	2	4	_aOrdinary Differential Equations.
650	2	4	_aSequences, Series, Summability.
700	1		_aPultr, Aleš. _eauthor.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9783034806350
856	4	0	_uhttp://dx.doi.org/10.1007/978-3-0348-0636-7
912			_aZDB-2-SMA
999			_c96320 _d96320