Elements of Real Analysis
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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.
Focusing on one of the main pillars of mathematics, this 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; theorems like mean value, Taylor's, and Darboux's; and power series. The final chapters focus on the more advanced theory of Lebesgue measure and integration.
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