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Record Nr. |
UNINA9910300099003321 |
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Autore |
Ghorpade Sudhir R |
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Titolo |
A Course in Calculus and Real Analysis / / by Sudhir R. Ghorpade, Balmohan V. Limaye |
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Pubbl/distr/stampa |
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Cham : , : Springer International Publishing : , : Imprint : Springer, , 2018 |
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ISBN |
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Edizione |
[2nd ed. 2018.] |
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Descrizione fisica |
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1 online resource (IX, 538 p.) |
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Collana |
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Undergraduate Texts in Mathematics, , 2197-5604 |
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Disciplina |
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Soggetti |
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Mathematical analysis |
Functions of real variables |
Sequences (Mathematics) |
Integral Transforms and Operational Calculus |
Real Functions |
Sequences, Series, Summability |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di contenuto |
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1. Numbers and Functions -- 2. Sequences -- 3. Continuity and Limits -- 4. Differentiation -- 5. Applications of Differentiation -- 6. Integration -- 7. Elementary Transcendental Functions -- 8. Applications and Approximations of Riemann Integrals -- 9. Infinite Series and Improper Integrals -- 10. Sequences and Series of Functions, Integrals Depending on a Parameter -- A. Construction of the Real Numbers -- B. Fundamental Theorem of Algebra -- References -- List of Symbols and Abbreviations -- Index. |
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Sommario/riassunto |
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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 |
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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 thelibrary of anyone involved in teaching calculus, or studying it seriously. N.J. Wildberger, Aust. Math. Soc. Gaz. |
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