Elementary analysis : the theory of calculus
著者
書誌事項
Elementary analysis : the theory of calculus
（Undergraduate texts in mathematics）
Springer-Verlag, c1980
- : us
- : gw
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注記
Bibliography: p. 258-259
Includes indexes
内容説明・目次
- 巻冊次
-
: us ISBN 9780387904597
内容説明
Designed for students having no previous experience with rigorous proofs, this text can be used immediately after standard calculus courses. It is highly recommended for anyone planning to study advanced analysis, as well as for future secondary school teachers. A limited number of concepts involving the real line and functions on the real line are studied, while many abstract ideas, such as metric spaces and ordered systems, are avoided completely. A thorough treatment of sequences of numbers is used as a basis for studying standard calculus topics, and optional sections invite students to study such topics as metric spaces and Riemann-Stieltjes integrals.
目次
Introduction.- Sequences.- Continuity.- Sequences and Series of Functions.- Differentiation.- Integration.- Appendix on Set Notation.- Selected Hints and Answers
- 巻冊次
-
: gw ISBN 9783540904595
内容説明
Designed for students having no previous experience with rigorous proofs, this text on analysis can be used immediately following standard calculus courses. It is highly recommended for anyone planning to study advanced analysis, for example complex variables, differential equations, Fourier analysis, numerical analysis, several variable calculus, and statistics. It is also recommended for future secondary school teachers. A limited number of concepts involving the real line and functions on the real line are studied. Many abstract ideas, such as metric spaces and ordered systems, are avoided. The least upper bound property is taken as an axiom and the order properties of the real line are exploited throughout. A thorough treatment of sequences of numbers is used as a basis for studying standard calculus topics. Optional sections invite students to study such topics as metric spaces and Riemann-Stieltjes integrals. Designed for students having no previous experience with rigorous proofs, this text can be used immediately after standard calculus courses. It is highly recommended for anyone planning to study advanced analysis, as well as for future secondary school teachers.
A limited number of concepts involving the real line and functions on the real line are studied, while many abstract ideas, such as metric spaces and ordered systems, are avoided completely. A thorough treatment of sequences of numbers is used as a basis for studying standard calculus topics, and optional sections invite students to study such topics as metric spaces and Riemann-Stieltjes integrals.
目次
Introduction.- Sequences.- Continuity.- Sequences and Series of Functions.- Differentiation.- Integration.- Appendix on Set Notation.- Selected Hints and Answers.- References.- Symbols Index.- Index.
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