000 03751nam a22004695i 4500
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
024 7 _a10.1007/978-0-8176-8289-7
_2doi
050 4 _aQA299.6-433
072 7 _aPBK
_2bicssc
072 7 _aMAT034000
_2bisacsh
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
912 _aZDB-2-SMA
999 _c100233
_d100233