00000cmm a22000004a 4500 UP-99796217611212583 Buklod 20241010115743.0 m go j cr |n |||auu|a 241010s2011 xxu o j eng d 9780387721774 (eBook) (iLib)UPD-00215704393 DMLR eng rda eng QA 241 B56 2011eb Bloch, Ethan D. 1956- author. The real numbers and real analysis [electronic resource] Ethan D. Bloch. New York, New York Springer New York 2011. 1 online resource illustrations. text rdacontent computer rdamedia online resource rdacarrier Preface.-To the Student.-To the Instructor.- 1. Construction of the Real Numbers -- 2. Properties of the Real Numbers -- 3. Limits and Continuity -- 4. Differentiation -- 5. Integration -- 6. Limits to Infinity.-7. Transcental Functions.-8. Sequences -- 9. Series -- 10. Sequences and Series of Functions -- Bibliography -- Index IP-based subscription, access limited to within on campus computer network. Access via Electronic Resources of the UPD University Library Website This text is a rigorous, detailed introduction to real analysis that presents the fundamentals with clear exposition and carefully written definitions, theorems, and proofs. The choice of material and the flexible organization, including three different entryways into the study of the real numbers, making it equally appropriate to undergraduate mathematics majors who want to continue in mathematics, and to future mathematics teachers who want to understand the theory behind calculus. The Real Numbers and Real Analysis is accessible to students who have prior experience with mathematical proofs and who have not previously studied real analysis. The text includes over 350 exercises. Key features of this textbook: - provides an unusually thorough treatment of the real numbers, emphasizing their importance as the basis of real analysis - presents material in an order resembling that of standard calculus courses, for the sake of student familiarity, and for helping future teachers use real analysis to better understand calculus - emphasizes the direct role of the Least Upper Bound Property in the study of limits, derivatives and integrals, rather than relying upon sequences for proofs; presents the equivalence of various important theorems of real analysis with the Least Upper Bound Property - includes a thorough discussion of some topics, such as decimal expansion of real numbers, transcendental functions, area and the number p, that relate to calculus but that are not always treated in detail in real analysis texts - offers substantial historical material in each chapter. This book will serve as an excellent one-semester text for undergraduates majoring in mathematics, and for students in mathematics education who want a thorough understanding of the theory behind the real number system and calcul Numbers, Real. Available for UP System via Springer Link. https://link.springer.com/book/10.1007/978-0-387-72177-4 FO UPD DMLR QA 241 B56 2011eb Electronic Resource