03745nam a22004575i 4500 978-0-8176-8289-7 DE-He213 20260521092034.0 cr nn 008mamaa 110923s2012 xxu| s |||| 0|eng d 9780817682897 99780817682897 10.1007/978-0-8176-8289-7 doi 515 23 Schinazi, Rinaldo B. author. From Calculus to Analysis [electronic resource] / by Rinaldo B. Schinazi. 1. Boston : Birkhäuser Boston : Imprint: Birkhäuser, 2012. X, 250 p. 7 illus. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda 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. 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. 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. MATHEMATICS. GLOBAL ANALYSIS (MATHEMATICS). SEQUENCES (MATHEMATICS). MATHEMATICS. ANALYSIS. SEQUENCES, SERIES, SUMMABILITY. APPROXIMATIONS AND EXPANSIONS. MEASURE AND INTEGRATION. SpringerLink (Online service) Springer eBooks Printed edition: 9780817682880 http://dx.doi.org/10.1007/978-0-8176-8289-7 Ver el texto completo en las instalaciones del CICY ZDB-2-SMA ddc ER 35807 35807 0 0 ddc 0 0 LE CICY CICY EL 2025-10-06 0 515 2025-10-06 08:44:40 2025-10-06 ER