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Catalogue Information
Field name	Details
Dewey Class	515
Title	From Calculus to Analysis ([Ebook]) / by Rinaldo B. Schinazi.
Author	Schinazi, Rinaldo B.
Other name(s)	SpringerLink (Online service)
Edition statement	1.st ed.
Publication	Boston : Birkhäuser
Publication	, 2012.
Physical Details	X, 250 p. 7 illus. : online resource.
ISBN	9780817682897
Summary Note	This 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.Â 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 principlesÂ of analysis; * Offers a straightforward introduction to the calculus basics such asÂ number systems, sequences, and series; * Carefully written book with a thoughtful perspective for students. From Calculus to Analysis prepares readers for their first analysis courseâimportant 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.:
Contents note	Preface -- 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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-0-8176-8289-7
Links to Related Works	Subject References: Analysis . Approximations and Expansions . Global analysis (Mathematics) . Mathematics . Measure and Integration . Sequences (Mathematics) . Sequences, Series, Summability . Authors: Schinazi, Rinaldo B. . Corporate Authors: SpringerLink (Online service) . Classification: 515 . 515 (DDC 23) .

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From Calculus to Analysis

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