Real analysis
Material type:
TextLanguage: English Publication details: New Delhi: Cambridge University Press, 2000 Description: xiii, 401p. PBKISBN: 9780521696241Subject(s): MATHEMATICS | MATHEMATICAL ANALYSISDDC classification: 517.13 Summary: This is a course in real analysis directed at advanced undergraduates and beginning graduate students in mathematics and related fields. Presupposing only a modest background in real analysis or advanced calculus, the book offers something to specialists and non-specialists. The course consists of three major topics: metric and normed linear spaces, function spaces, and Lebesgue measure and integration on the line. In an informal style, the author gives motivation and overview of new ideas, while supplying full details and proofs. He includes historical commentary, recommends articles for specialists and non-specialists, and provides exercises and suggestions for further study. This text for a first graduate course in real analysis was written to accommodate the heterogeneous audiences found at the masters level: students interested in pure and applied mathematics, statistics, education, engineering, and economics.
| Item type | Current library | Call number | Status | Date due | Barcode |
|---|---|---|---|---|---|
Book
|
NISER LIBRARY | 517.13 CAR-R (Browse shelf(Opens below)) | Available | 24703 | |
|
Book
|
NISER LIBRARY | 517.13 CAR-R (Browse shelf(Opens below)) | Checked out to Alokjeet Sahoo (2211017) | 24/05/2024 | 24704 |
|
Book
|
NISER LIBRARY | 517.13 CAR-R (Browse shelf(Opens below)) | Available | 24705 | |
|
Book
|
NISER LIBRARY | 517.13 CAR-R (Browse shelf(Opens below)) | Checked out to S Mahesh (2111097) | 11/05/2024 | 24706 |
|
Book
|
NISER LIBRARY | 517.13 CAR-R (Browse shelf(Opens below)) | Available | 24707 | |
|
Book
|
NISER LIBRARY | 517.13 CAR-R (Browse shelf(Opens below)) | R (REFERENCE) | 21068 | |
Gift books
|
SMS Library | 517.13 CAR-R (Browse shelf(Opens below)) | Available | G1026 | |
|
Gift books
|
SMS Library | 517.13 CAR-R (Browse shelf(Opens below)) | Available | G1027 |
Contents
Preface
PART ONE - METRIC SPACES
1 - Calculus Review
2 - Countable and Uncountable Sets
3 - Metrics and Norms
4 - Open Sets and Closed Sets
5 - Continuity
6 - Connectedness
7 - Completeness
8 - Compactness
9 - Category
PART TWO - FUNCTION SPACES
10 - Sequences of Functions
11 - The Space of Continuous Functions
12 - The Stone–Weierstrass Theorem
13 - Functions of Bounded Variation
14 - The Riemann–Stieltjes Integral
15 - Fourier Series
PART THREE - LEBESGUE MEASURE AND INTEGRATION
16 - Lebesgue Measure
17 - Measurable Functions
18 - The Lebesgue Integral
19 - Additional Topics
20 - Differentiation
References
Symbol Index
Topic Index
This is a course in real analysis directed at advanced undergraduates and beginning graduate students in mathematics and related fields. Presupposing only a modest background in real analysis or advanced calculus, the book offers something to specialists and non-specialists. The course consists of three major topics: metric and normed linear spaces, function spaces, and Lebesgue measure and integration on the line. In an informal style, the author gives motivation and overview of new ideas, while supplying full details and proofs. He includes historical commentary, recommends articles for specialists and non-specialists, and provides exercises and suggestions for further study. This text for a first graduate course in real analysis was written to accommodate the heterogeneous audiences found at the masters level: students interested in pure and applied mathematics, statistics, education, engineering, and economics.
There are no comments on this title.