A first course in real analysis
著者
書誌事項
A first course in real analysis
（Undergraduate texts in mathematics）
Springer-Verlag, c1991
2nd ed
- : us
- : gw
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注記
Includes index
内容説明・目次
- 巻冊次
-
: us ISBN 9780387974378
内容説明
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.
目次
- 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.
- 巻冊次
-
: gw ISBN 9783540974376
内容説明
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.
目次
- 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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