Analysis, II II [electronic resource] / Terence Tao.
Tao, Terence| Call Number | 515 |
| Author | Tao, Terence. |
| Title | Analysis, II Terence Tao. |
| Edition | 2nd ed. |
| Publication | [S.l.] : Hindustan Book Agency, 2009. |
| Physical Description | 238 p. |
| Series | Texts and Readings in Mathematics ; 38 |
| Contents | Analysis, II -- Contents -- Preface to the First Edition -- Preface to the Second Edition -- Chapter 12: Metric Spaces -- Chapter 13: Continuous Functions on Metric Spaces -- Chapter 14: Uniform Convergence -- Chapter 15: Power Series -- Chapter 16: Fourier Series -- Chapter 17: Several Variable Differential Calculus -- Chapter 18: Lebesgue Measure -- Chapter 19: Lebesgue Integration -- Index -- Texts and Readings in Mathematics. |
| Summary | This is part one 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 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 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. The second edition has been extensively revised and updated. |
| Subject | MATHEMATICAL ANALYSIS |
| Multimedia |
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$a Analysis, II -- Contents -- Preface to the First Edition -- Preface to the Second Edition -- Chapter 12: Metric Spaces -- Chapter 13: Continuous Functions on Metric Spaces -- Chapter 14: Uniform Convergence -- Chapter 15: Power Series -- Chapter 16: Fourier Series -- Chapter 17: Several Variable Differential Calculus -- Chapter 18: Lebesgue Measure -- Chapter 19: Lebesgue Integration -- Index -- Texts and Readings in Mathematics.
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| Summary | This is part one 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 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 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. The second edition has been extensively revised and updated. |
| Contents | Analysis, II -- Contents -- Preface to the First Edition -- Preface to the Second Edition -- Chapter 12: Metric Spaces -- Chapter 13: Continuous Functions on Metric Spaces -- Chapter 14: Uniform Convergence -- Chapter 15: Power Series -- Chapter 16: Fourier Series -- Chapter 17: Several Variable Differential Calculus -- Chapter 18: Lebesgue Measure -- Chapter 19: Lebesgue Integration -- Index -- Texts and Readings in Mathematics. |
| Subject | MATHEMATICAL ANALYSIS |
| Multimedia |