000 | 03751nam a22004695i 4500 | ||
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001 | 978-0-8176-8289-7 | ||
003 | DE-He213 | ||
005 | 20140220083227.0 | ||
007 | cr nn 008mamaa | ||
008 | 110923s2012 xxu| s |||| 0|eng d | ||
020 |
_a9780817682897 _9978-0-8176-8289-7 |
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024 | 7 |
_a10.1007/978-0-8176-8289-7 _2doi |
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050 | 4 | _aQA299.6-433 | |
072 | 7 |
_aPBK _2bicssc |
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072 | 7 |
_aMAT034000 _2bisacsh |
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082 | 0 | 4 |
_a515 _223 |
100 | 1 |
_aSchinazi, Rinaldo B. _eauthor. |
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245 | 1 | 0 |
_aFrom Calculus to Analysis _h[electronic resource] / _cby Rinaldo B. Schinazi. |
250 | _a1. | ||
264 | 1 |
_aBoston : _bBirkhäuser Boston : _bImprint: Birkhäuser, _c2012. |
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300 |
_aX, 250 p. 7 illus. _bonline resource. |
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336 |
_atext _btxt _2rdacontent |
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337 |
_acomputer _bc _2rdamedia |
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338 |
_aonline resource _bcr _2rdacarrier |
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347 |
_atext file _bPDF _2rda |
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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 |
912 | _aZDB-2-SMA | ||
999 |
_c100233 _d100233 |