000			03745nam a22004575i 4500
001			978-0-8176-8289-7
003			DE-He213
005			20251006084440.0
007			cr nn 008mamaa
008			110923s2012 xxu| s |||| 0|eng d
020			_a9780817682897
020			_a99780817682897
024	7		_a10.1007/978-0-8176-8289-7 _2doi
082	0	4	_a515 _223
100	1		_aSchinazi, Rinaldo B. _eauthor.
245	1	0	_aFrom Calculus to Analysis _h[electronic resource] / _cby Rinaldo B. Schinazi.
250			_a1.
264		1	_aBoston : _bBirkhäuser Boston : _bImprint: Birkhäuser, _c2012.
300			_aX, 250 p. 7 illus. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
505	0		_aPreface -- Ch. 1 Number Systems -- 1.1 The algebra of the reals -- 1.2 Natural numbers and integers -- .1.3 Rational numbers and real numbers -- 1.4 Power functions -- Ch. 2 Sequences and Series -- 2.1 Sequences -- 2.2 Montone sequences, Bolzano-Weirestrass theorem and operations on limits -- 2.3 Series -- 2.4 Absolute convergence -- Ch. 3 Power series and special functions.-3.1 Power series.-3.2 Tigonometric functions -- 3.3 Inverse trigonometric functions -- 3.4 Exponential and logarithmic functions -- Ch 4 Fifty Ways to Estimate the Number pi.-4.1 Power series expansions -- 4.2 Wallis' integrals, Euler's formula, and Stirling's formula.-4.3 Convergence of infinite products -- 4.4 The number pi is irrational -- Ch. 5 Continuity, Limits, and Differentiation -- 5.1 Continuity -- 5.2 Limits of functions and derivatives -- 5.3 Algebra of derivatives and mean value theorems -- 5.4 Intervals, continuity, and inverse functions -- Ch. 6 Riemann Integration -- 6.1 Construction of the integral -- 6.2 Properties of the integral -- 6.3 Uniform continuity -- Ch 7 Decimal Represenation of Numbers -- Ch 8 Countable and Uncountable Sets -- Further Readings -- Index.
520			_aThis comprehensive textbook is intended for a two-semester sequence in analysis. The first four chapters present a practical introduction to analysis by using the tools and concepts of calculus. The last five chapters present a first course in analysis. The presentation is clear and concise, allowing students to master the calculus tools that are crucial in understanding analysis. Key features: * Contains numerous exercises; * Provides unique examples, such as many ways to estimate the number Pi; * Introduces the basic principles of analysis; * Offers a straightforward introduction to the calculus basics such as number systems, sequences, and series; * Carefully written book with a thoughtful perspective for students. From Calculus to Analysis prepares readers for their first analysis course-important because many undergraduate programs traditionally require such a course. Undergraduates and some advanced high-school seniors will find this text a useful and pleasant experience in the classroom or as a self-study guide. The only prerequisite is a standard calculus course.
650		0	_aMATHEMATICS.
650		0	_aGLOBAL ANALYSIS (MATHEMATICS).
650		0	_aSEQUENCES (MATHEMATICS).
650	1	4	_aMATHEMATICS.
650	2	4	_aANALYSIS.
650	2	4	_aSEQUENCES, SERIES, SUMMABILITY.
650	2	4	_aAPPROXIMATIONS AND EXPANSIONS.
650	2	4	_aMEASURE AND INTEGRATION.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9780817682880
856	4	0	_uhttp://dx.doi.org/10.1007/978-0-8176-8289-7 _zVer el texto completo en las instalaciones del CICY
912			_aZDB-2-SMA
942			_2ddc _cER
999			_c59874 _d59874