000			03774nam a22004935i 4500
001			978-3-319-42755-3
003			DE-He213
005			20200421112557.0
007			cr nn 008mamaa
008			161004s2016 gw | s |||| 0|eng d
020			_a9783319427553 _9978-3-319-42755-3
024	7		_a10.1007/978-3-319-42755-3 _2doi
050		4	_aQA76.9.M35
072		7	_aUYA _2bicssc
072		7	_aUYAM _2bicssc
072		7	_aCOM018000 _2bisacsh
072		7	_aMAT003000 _2bisacsh
082	0	4	_a004.0151 _223
100	1		_aR�omisch, Werner. _eauthor.
245	1	0	_aMathematical Analysis and the Mathematics of Computation _h[electronic resource] / _cby Werner R�omisch, Thomas Zeugmann.
264		1	_aCham : _bSpringer International Publishing : _bImprint: Springer, _c2016.
300			_aXXIII, 703 p. 52 illus., 32 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		_aSets, Structures, Numbers -- Metric Spaces -- Continuous Functions in Metric Spaces -- Linear Normed Spaces, Linear Operators -- The Differential Calculus -- Applications of the Differential Calculus -- The Integral Calculus -- Linear Integral Operators -- Inner Product Spaces -- Approximative Representation of Functions -- Ordinary Differential Equations -- Discretization of Operator Equations -- Numerical Solution of Ordinary Differential Equations.
520			_aThis book is a comprehensive, unifying introduction to the field of mathematical analysis and the mathematics of computing. It develops the relevant theory at a modern level and it directly relates modern mathematical ideas to their diverse applications. The authors develop the whole theory. Starting with a simple axiom system for the real numbers, they then lay the foundations, developing the theory, exemplifying where it's applicable, in turn motivating further development of the theory. They progress from sets, structures, and numbers to metric spaces, continuous functions in metric spaces, linear normed spaces and linear mappings; and then differential calculus and its applications, the integral calculus, the gamma function, and linear integral operators. They then present important aspects of approximation theory, including numerical integration. The remaining parts of the book are devoted to ordinary differential equations, the discretization of operator equations, and numerical solutions of ordinary differential equations. This textbook contains many exercises of varying degrees of difficulty, suitable for self-study, and at the end of each chapter the authors present more advanced problems that shed light on interesting features, suitable for classroom seminars or study groups. It will be valuable for undergraduate and graduate students in mathematics, computer science, and related fields such as engineering. This is a rich field that has experienced enormous development in recent decades, and the book will also act as a reference for graduate students and practitioners who require a deeper understanding of the methodologies, techniques, and foundations.
650		0	_aComputer science.
650		0	_aComputer science _xMathematics.
650		0	_aMathematical analysis.
650		0	_aAnalysis (Mathematics).
650	1	4	_aComputer Science.
650	2	4	_aMathematics of Computing.
650	2	4	_aAnalysis.
700	1		_aZeugmann, Thomas. _eauthor.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9783319427539
856	4	0	_uhttp://dx.doi.org/10.1007/978-3-319-42755-3
912			_aZDB-2-SCS
942			_cEBK
999			_c59231 _d59231