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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Complex analysis
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Real Analysis and Infinity (Hardcover)
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Real Analysis and Infinity (Hardcover)
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Real Analysis and Infinity presents the essential topics for a
first course in real analysis with an emphasis on the role of
infinity in all of the fundamental concepts. After introducing
sequences of numbers, it develops the set of real numbers in terms
of Cauchy sequences of rational numbers, and uses this development
to derive the important properties of real numbers like
completeness. The book then develops the concepts of continuity,
derivative, and integral, and presents the theory of infinite
sequences and series of functions. Topics discussed are
wide-ranging and include the convergence of sequences, definition
of limits and continuity via converging sequences, and the
development of derivative. The proofs of the vast majority of
theorems are presented and pedagogical considerations are given
priority to help cement the reader's knowledge. Preliminary
discussion of each major topic is supplemented with examples and
diagrams, and historical asides. Examples follow most major results
to improve comprehension, and exercises at the end of each chapter
help with the refinement of proof and calculation skills.
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