Elements of real analysis
著者
書誌事項
Elements of real analysis
（Monographs and textbooks in pure and applied mathematics, 284）
Chapman & Hall/CRC, c2007
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注記
"Based on lecture notes prepared (in Arabic) by the authors, ... at King Saud University (KSU)"--Pref., p. [vii]
Includes bibliographical references (p. [429]) and index
内容説明・目次
内容説明
Focusing on one of the main pillars of mathematics, Elements of Real Analysis provides a solid foundation in analysis, stressing the importance of two elements. The first building block comprises analytical skills and structures needed for handling the basic notions of limits and continuity in a simple concrete setting while the second component involves conducting analysis in higher dimensions and more abstract spaces.
Largely self-contained, the book begins with the fundamental axioms of the real number system and gradually develops the core of real analysis. The first few chapters present the essentials needed for analysis, including the concepts of sets, relations, and functions. The following chapters cover the theory of calculus on the real line, exploring limits, convergence tests, several functions such as monotonic and continuous, power series, and theorems like mean value, Taylor's, and Darboux's. The final chapters focus on more advanced theory, in particular, the Lebesgue theory of measure and integration.
Requiring only basic knowledge of elementary calculus, this textbook presents the necessary material for a first course in real analysis. Developed by experts who teach such courses, it is ideal for undergraduate students in mathematics and related disciplines, such as engineering, statistics, computer science, and physics, to understand the foundations of real analysis.
目次
Preface. Preliminaries. Real Numbers. Sequences. Infinite Series. Limit of a Function. Continuity. Differentiation. The Riemann Integral. Sequences and Series of Functions. Lebesgue Measure. Lebesgue Integration. References. Notation. Index.
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