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Analysis II [electronic resource] : Fourth Edition / by Terence Tao

Author
Tao, Terence
Published
Singapore : Springer Nature Singapore : Imprint: Springer, 2022.
Edition
2nd ed. 2022.
Physical Description
X, 210 p. online resource
Additional Creators
SpringerLink (Online service)
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Series
Contents
Chapter 1. Metric Spaces -- Chapter 2. Continuous functions on metric spaces -- Chapter 3. Uniform convergence -- Chapter 4. Power series -- Chapter 5. Fourier series -- Chapter 6. Several variable differential calculus -- Chapter 7. Lebesgue measure -- Chapter 8. Lebesgue integration.
Summary
This is the second 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 taught in two quarters of twenty-five to thirty lectures each.
Subject(s)
ISBN
9789811972843
Digital File Characteristics
text file PDF
Part Of
Springer Nature eBook
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