A first course in real analysis
Author(s)
Bibliographic Information
A first course in real analysis
（Undergraduate texts in mathematics）
Springer-Verlag, c1991
2nd ed
- : us
- : gw
Available at / 61 libraries
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Hokkaido University, Library, Graduate School of Science, Faculty of Science and School of Science図書
DC19:515/P9462070204597
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Note
Includes index
Description and Table of Contents
- Volume
-
: us ISBN 9780387974378
Description
Many changes have been made in this second edition of A First Course in Real Analysis. The most noticeable is the addition of many problems and the inclusion of answers to most of the odd-numbered exercises. The book's readability has also been improved by the further clarification of many of the proofs, additional explanatory remarks, and clearer notation.
Table of Contents
- 1: The Real Number System. 2: Continuity and Limits. 3: Basic Properties of Functions on R. 4: Elementary Theory of Differentiation. 5: Elementary Theory of Integration. 6: Elementary Theory of Metric Spaces. 7: Differentiation in R. 8: Integration in R. 9: Infinite Sequences and Infinite Series. 10: Fourier Series. 11: Functions Defined by Integrals
- Improper Integrals. 12: The Riemann-Stieltjes Integral and Functions of Bounded Variation. 13: Contraction Mappings, Newton's Method, and Differential Equations. 14: Implicit Function Theorems and Lagrange Multipliers. 15: Functions on Metric Spaces
- Approximation. 16: Vector Field Theory
- the Theorems of Green and Stokes. Appendices.
- Volume
-
: gw ISBN 9783540974376
Description
Many changes have been made in this second edition of "A First Course in Real Analysis". The most noticeable is the addition of many problems and the inclusion of answers to most of the odd-numbered exercises. The book's readability has also been improved by the further clarification of many of the proofs, additional explanatory remarks, and clearer notation. This textbook on mathematics is intended for undergraduate students in mathematics.
Table of Contents
- The Real Number System.- Continuity and Limits.- Basic Properties of Functions on R.- Elementary Theory of Differentiation.- Elementary Theory of Integration.- Elementary Theory of Metric Spaces.- Differentiation in R.- Integration in R.- Infinite Sequences and Infinite Series.- Fourier Series.- Functions Defined by Integrals.-Improper Integrals.- The Riemann-Stieltjes Integral and Functions of Bounded Variation.- Contraction Mappings, Newton's Method, and Differential Equations.- Implicit Function Theorems and Lagrange Multipliers.- Functions on Metric Spaces.- Approximation.- Vector Field Theory
- the Theorems of Green and Stokes. Appendices.
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