000			03816nam a22004695i 4500
001			978-0-8176-8292-7
003			DE-He213
005			20140220083227.0
007			cr nn 008mamaa
008			111216s2012 xxu| s |||| 0|eng d
020			_a9780817682927 _9978-0-8176-8292-7
024	7		_a10.1007/978-0-8176-8292-7 _2doi
050		4	_aQA299.6-433
072		7	_aPBK _2bicssc
072		7	_aMAT034000 _2bisacsh
082	0	4	_a515 _223
100	1		_aPonnusamy, S. _eauthor.
245	1	0	_aFoundations of Mathematical Analysis _h[electronic resource] / _cby S. Ponnusamy.
250			_a1.
264		1	_aBoston, MA : _bBirkhäuser Boston : _bImprint: Birkhäuser, _c2012.
300			_aXV, 570p. 205 illus. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
505	0		_aReal Number System -- Sequences: Convergence and Divergence -- Limits, Continuity, and Differentiability -- Applications of Differentiability -- Series: Convergence and Divergence -- Definite and Indefinite Integrals -- Improper Integrals and Applications of Riemann Integrals -- Power Series -- Uniform Convergence of Sequences of Functions -- Fourier Series and Applications -- Functions of Bounded Variation and Riemann-Stieltjes Integrals -- References -- Index of Special Notations -- Hints for Selected Questions and Exercises -- Index.
520			_aMathematical analysis is fundamental to the undergraduate curriculum not only because it is the stepping stone for the study of advanced analysis, but also because of its applications to other branches of mathematics, physics, and engineering at both the undergraduate and graduate levels. This self-contained textbook consists of eleven chapters, which are further divided into sections and subsections. Each section includes a careful selection of special topics covered that will serve to illustrate the scope and power of various methods in real analysis. The exposition is developed with thorough explanations, motivating examples, and illustrations conveying geometric intuition in a pleasant and informal style to help readers grasp difficult concepts. Key features include: * “Questions and Exercises” are provided at the end of each section, covering a broad spectrum of content with various levels of difficulty; * Some of the exercises are routine in nature while others are interesting, instructive, and challenging with hints provided for selected exercises; * Covers a broad spectrum of content with a range of difficulty that will enable students to learn techniques and standard analysis tools; * Introduces convergence, continuity, differentiability, the Riemann integral, power series, uniform convergence of sequences and series of functions, among other topics; * Examines various important applications throughout the book; * Figures throughout the book to demonstrate ideas and concepts are drawn using Mathematica. Foundations of Mathematical Analysis is intended for undergraduate students and beginning graduate students interested in a fundamental introduction to the subject. It may be used in the classroom or as a self-study guide without any required prerequisites.
650		0	_aMathematics.
650		0	_aGlobal analysis (Mathematics).
650		0	_aFourier analysis.
650	1	4	_aMathematics.
650	2	4	_aAnalysis.
650	2	4	_aApplications of Mathematics.
650	2	4	_aApproximations and Expansions.
650	2	4	_aFourier Analysis.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9780817682910
856	4	0	_uhttp://dx.doi.org/10.1007/978-0-8176-8292-7
912			_aZDB-2-SMA
999			_c100234 _d100234