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Bücher Englische Bücher Wissen & Bildung Naturwissenschaft, Medizin, Informatik, Technik Mathematik Analysis A Course in Calculus and Real Analysis
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A Course in Calculus and Real Analysis
Sudhir R. Ghorpade, Balmohan V. Limaye (Broschiert, Englisch)
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Beschreibung
Offering a unified exposition of calculus and classical real analysis, this textbook presents a meticulous introduction to single‐variable calculus. Throughout, the exposition makes a distinction between the intrinsic geometric definition of a notion and its analytic characterization, establishing firm foundations for topics often encountered earlier without proof. Each chapter contains numerous… examples and a large selection of exercises, as well as a “Notes and Comments” section, which highlights distinctive features of the exposition and provides additional references to relevant literature. This second edition contains substantial revisions and additions, including several simplified proofs, new sections, and new and revised figures and exercises. A new chapter discusses sequences and series of real‐valued functions of a real variable, and their continuous counterpart: improper integrals depending on a parameter. Two new appendices cover a construction of the real numbers using Cauchy sequences, and a self‐contained proof of the Fundamental Theorem of Algebra. In addition to the usual prerequisites for a first course in single‐variable calculus, the reader should possess some mathematical maturity and an ability to understand and appreciate proofs. This textbook can be used for a rigorous undergraduate course in calculus, or as a supplement to a later course in real analysis. The authors’ A Course in Multivariable Calculus is an ideal companion volume, offering a natural extension of the approach developed here to the multivariable setting. From reviews: [The first edition is] a rigorous, well-presented and original introduction to the core of undergraduate mathematics — first-year calculus. It develops this subject carefully from a foundation of high-school algebra, with interesting improvements and insights rarely found in other books. […] This book is a tour de force, and a necessary addition to the library of anyone involved in teaching calculus, or studying it seriously. N.J. Wildberger, Aust. Math. Soc. Gaz. Dieses Produkt haben wir gerade leider nicht auf Lager.
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Technische Daten
Erscheinungsdatum
28.11.2021
Sprache
Englisch
EAN
9783030827410
Herausgeber
Springer International Publishing
Serien- oder Bandtitel
Undergraduate Texts in Mathematics
Sonderedition
Nein
Autor
Sudhir R. Ghorpade, Balmohan V. Limaye
Seitenanzahl
538
Auflage
2
Einbandart
Broschiert
Schlagwörter
Honors Calculus textbook, Introduction to Real Analysis, Ghorpade Limaye textbook, real analysis textbook, Real Functions, Sequences and Series, Continuity and Limits, Differentiation, Integration, transcendental functions, Riemann integrals, Infinite Series
Thema-Inhalt
PBKL - Integralrechnung und -gleichungen
PBKB - Reelle Analysis, Real-Variablen
PBK - Mathematische Analysis, allgemein
Höhe
235 mm
Breite
15.5 cm
Hersteller: Springer Nature Customer Service Center GmbH, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com
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