A first course in real analysis
著者
書誌事項
A first course in real analysis
（Undergraduate texts in mathematics）
Springer Science+Business Media, [20--], c1991
2nd ed
- : [pbk.]
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注記
"Originally published by Springer-Verlag New York Inc. in 1991"--T.p. verso
"Softcover reprint of the hardcover 2nd edition 1991"--T.p. verso
Includes bibliographical and index (p. 529-534)
内容説明・目次
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.
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