A Course in Calculus and Real Analysis. 2nd ed. 2018

種類:

電子ブック

責任表示:

by Sudhir R. Ghorpade, Balmohan V. Limaye

出版情報:

Cham : Springer International Publishing : Imprint: Springer, 2018

著者名:

• Ghorpade, Sudhir R.
• Limaye, Balmohan V.
• SpringerLink (Online service)

シリーズ名:

Undergraduate Texts in Mathematics ;

ISBN:

9783030014001 [3030014002]    

注記:

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.
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 sel

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