UID:
edoccha_9958094978102883
Format:
1 online resource (407 pages)
ISBN:
1-281-76338-1
,
9786611763381
,
0-08-087318-9
Series Statement:
Pure and applied mathematics ; v.1
Note:
Description based upon print version of record.
,
Cover; TOCContents; Preface to the Enlarged and Corrected Printing; Preface; Notations; CHChapter I. Elements of the Theory of Sets; 1.1. Elements and sets; 1.2. Boolean algebra; 1.3. Product of two sets; 1.4. Mappings; 1.5. Direct and inverse images; 1.6. Surjective, injective, and bijective mappings; 1.7. Composition of mappings; 1.8. Families of elements. Union, intersection, and products of families of sets. Equivalence relations; 1.9. Denumerable sets; CHChapter II. Real Numbers; 2.1. Axioms of the real numbers; 2.2. Order properties of the real numbers
,
2.3. Least upper bound and greatest lower boun; Chapter III. Metric Spaces; 3.1. Distances and metric spaces; 3.2. Examples of distances; 3.3. Isometries; 3.4. Balls, spheres, diameter; 3.5. Open sets; 3.6. Neighborhoods; 3.7. Interior of a set; 3.8. Closed sets, cluster points, closure of a set; 3.9. Dense subsets; separable spaces; 3.10. Subspaces of a metric space; 3.11. Continuous mappings; 3.12. Homeomorphisms. Equivalent distances; 3.13. Limits; 3.14. Cauchy sequences, complete spaces; 3.15. Elementary extension theorems; 3.16. Compact spaces; 3.17. Compact sets
,
3.18. Locally compact spaces; 3.19. Connected spaces and connected sets; 3.20. Product of two metric spaces; Chapter IV. Additional Properties of the Real Line; 4.1 . Continuity of algebraic operations; 4.2. Monotone functions; 4.3. Logarithms and exponentials; 4.4. Complex numbers; 4.5. The Tietze-Urysohn extension theorem; Chapter V. Normed Spaces; 5.1. Normed spaces and Banach spaces; 5.2. Series in a normed space; 5.3. Absolutely convergent series; 5.4. Subspaces and finite products of normed spaces; 5.5. Condition of continuity of a multilinear mapping; 5.6. Equivalent norms
,
5.7. Spaces of continuous multilinear mappings; 5.8. Closed hyperplanes and continuous linear forms; 5.9. Finite dimensional normed spaces; 5.10. Separable normed spaces; Chapter VI. Hilbert Spaces; 6.1. Hermitian forms; 6.2. Positive hermitian forms; 6.3. Orthogonal projection on a complete subspace; 6.4. Hilbert sum of Hilbert spaces; 6.5. Orthonormal systems; 6.6. Orthonormalizat; CHChapter VII. Spaces of Continuous Functions; 7.1. Spaces of bounded functions; 7.2. Spaces of bounded continuous functions; 7.3. The Stone-Weierstrass approximation theorem; 7.4. Applications
,
7.5. Equicontinuous sets7.6. Regulated functions; Chapter VIII. Differential Calculus; 8.1. Derivative of a continuous mapping; 8.2. Formal rules of derivation; 8.3. Derivatives in spaces of continuous linear functions; 8.4. Derivatives of functions of one variable; 8.5. The mean value theorem; 8.6. Applications of the mean value theorem; 8.7. Primitives and integrals; 8.8. Application: the number e; 8.9. Partial derivatives; 8.10. Jacobians; 8.11. Derivative of an integral depending on a parameter; 8.12. Higher derivatives; 8.13. Differential operators; 8.14. Taylor's formula; Chapter IX. Analytic Functions
Additional Edition:
ISBN 0-12-215550-5
Language:
English
