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Analysis II: Third Edition
 
Terence Tao University of California, Los Angeles
A publication of Hindustan Book Agency
Front Cover for Analysis II
This title is not currently available
Front Cover for Analysis II
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Analysis II: Third Edition
Terence Tao University of California, Los Angeles
A publication of Hindustan Book Agency
This title is not currently available
  • Book Details
     
     
    Hindustan Book Agency
    Volume: 672014; 236 pp
    MSC: Primary 26;

    Now available in Fourth Edition: HIN/83

    This is part two of a two-volume introduction to real analysis and is intended for honours undergraduates who have already been exposed to calculus. The emphasis is on rigour and on foundations. The material starts at the very beginning—the construction of the number systems and set theory—then goes on to the basics of analysis (limits, series, continuity, differentiation, Riemann integration), through to power series, several variable calculus and Fourier analysis, and finally to the Lebesgue integral. These are almost entirely set in the concrete setting of the real line and Euclidean spaces, although there is some material on abstract metric and topological spaces. There are also appendices on mathematical logic and the decimal system. The entire text (omitting some less central topics) can be taught in two quarters of twenty-five to thirty lectures each.

    The course material is deeply intertwined with the exercises, as it is intended that the student actively learn the material (and practice thinking and writing rigorously) by proving several of the key results in the theory.

    In the third edition, several typos and other errors have been corrected and a few new exercises have been added.

    Readership

    Undergraduate and graduate students interested in analysis.

  • Reviews
     
     
    • From a review of the first edition:

      …it would be an error not to stick very close to the text — it's very well crafted indeed and deviating from the score would mean an unacceptable dissonance.

      I hope to use Analysis I, II in an honors course myself, when the opportunity arises.

      Michael Berg, for MAA Reviews
Volume: 672014; 236 pp
MSC: Primary 26;

Now available in Fourth Edition: HIN/83

This is part two of a two-volume introduction to real analysis and is intended for honours undergraduates who have already been exposed to calculus. The emphasis is on rigour and on foundations. The material starts at the very beginning—the construction of the number systems and set theory—then goes on to the basics of analysis (limits, series, continuity, differentiation, Riemann integration), through to power series, several variable calculus and Fourier analysis, and finally to the Lebesgue integral. These are almost entirely set in the concrete setting of the real line and Euclidean spaces, although there is some material on abstract metric and topological spaces. There are also appendices on mathematical logic and the decimal system. The entire text (omitting some less central topics) can be taught in two quarters of twenty-five to thirty lectures each.

The course material is deeply intertwined with the exercises, as it is intended that the student actively learn the material (and practice thinking and writing rigorously) by proving several of the key results in the theory.

In the third edition, several typos and other errors have been corrected and a few new exercises have been added.

Readership

Undergraduate and graduate students interested in analysis.

  • From a review of the first edition:

    …it would be an error not to stick very close to the text — it's very well crafted indeed and deviating from the score would mean an unacceptable dissonance.

    I hope to use Analysis I, II in an honors course myself, when the opportunity arises.

    Michael Berg, for MAA Reviews
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