A course in real analysis /
Now in its second editon, A Course in Real Analysis provides a rigorous treatment of the foundations of differential and integral calculus. It proceeds gradually from an axiomatic characterization of the real number system to the study of differentiation and integration on m-dimensional surfaces. Pr...
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| Format: | eBook |
| Language: | English |
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Boca Raton :
Chapman and Hall/CRC,
2026.
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| Edition: | Second edition. |
| Series: | Textbooks in mathematics (Boca Raton, Fla.)
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| Online Access: | Connect to the full text of this electronic book |
| Summary: | Now in its second editon, A Course in Real Analysis provides a rigorous treatment of the foundations of differential and integral calculus. It proceeds gradually from an axiomatic characterization of the real number system to the study of differentiation and integration on m-dimensional surfaces. Proofs of theorems are given in detail, and many examples are provided to illustrate the concepts expressed in the theorems.The book consists of three parts. Part I treats the calculus of functions of one variable. Traditional topics such as sequences, continuity, differentiability, Riemann integrability, numerical series, and the convergence of sequences and series of functions are covered. Optional sections on Stirling's formula, Riemann-Stieltjes integration, and other topics are also included.The second part focuses on functions of several variables. It introduces the topological ideas (such as compact and connected sets) needed to describe analytical properties of multivariable functions. This part also discusses differentiability and integrability of multivariable functions, and it develops the theory of differential forms on surfaces in Rn.Many proofs and explanations in the first edition have been revised, and details have been added to clarify the exposition. Part III contains the Appendices on set theory and linear algebra, as well as solutions to some of the exercises are offered, while a full Solutions Manual contains complete solutions to all exercises for qualifying instructors. |
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| Physical Description: | 1 online resource (591 pages) : illustrations (black and white). |
| Bibliography: | Includes bibliographical references and index. |
| ISBN: | 9781040608098 1040608094 9781003629382 1003629385 9781040579213 1040579213 |