Analysis I
Fourth Edition
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Beschreibung
This is the first book of a two-volume textbook on real analysis. Both the volumes—Analysis I and Analysis II—are intended for honors undergraduates who have already been exposed to calculus. The emphasis is on rigor and foundations. The material starts at the very beginning—the construction of number systems and set theory (Analysis I, Chaps. 1–5), then on to the basics of analysis such as limits, series, continuity, differentiation, and Riemann integration (Analysis I, Chaps. 6–11 on Euclidean spaces, and Analysis II, Chaps. 1–3 on metric spaces), through power series, several variable calculus, and Fourier analysis (Analysis II, Chaps. 4–6), and finally to the Lebesgue integral (Analysis II, Chaps. 7–8). There are appendices on mathematical logic and the decimal system. The entire text (omitting some less central topics) is in two quarters of twenty-five to thirty lectures each.
Presents a foundation text on real analysis for undergraduate and graduate students of mathematics Emphasizes on number systems and set theory than in comparable analysis Is the first book of a two-volume textbook on real analysis
Autor*in
Terence Tao
Themen in »Analysis I«
natural numbers set theory integers and rationals real numbers limits of sequences series continuous functions differentiation of functions Riemann integral
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