Real and complex analysis. (Record no. 40351)
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| 000 -LEADER | |
|---|---|
| fixed length control field | 05717nam a2200325 a 4500 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | CUTN |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20231114160440.0 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 900615s1987 nyu b 00110 eng |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9780070619876 |
| 041 ## - LANGUAGE CODE | |
| Language | English |
| 082 ## - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 515 |
| Item number | RUD |
| 090 ## - LOCALLY ASSIGNED LC-TYPE CALL NUMBER (OCLC); LOCAL CALL NUMBER (OCLC) | |
| Classification number (OCLC) (R) ; Classification number, CALL (RLIN) (NR) | QA300 |
| Local cutter number (OCLC) ; Book number/undivided call number, CALL (RLIN) | Rud |
| 100 10 - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Rudin, Walter |
| 245 10 - TITLE STATEMENT | |
| Title | Real and complex analysis. |
| Statement of responsibility, etc | / Walter Rudin. |
| 250 ## - EDITION STATEMENT | |
| Edition statement | 3rd ed. |
| 260 0# - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) | |
| Place of publication, distribution, etc | New York |
| Name of publisher, distributor, etc | : McGraw-Hill |
| Date of publication, distribution, etc | , c1987. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | xiv, 416 p. |
| Dimensions | ; 24 cm. |
| 500 ## - GENERAL NOTE | |
| General note | Cover title: Real & complex analysis. |
| 500 ## - GENERAL NOTE | |
| General note | Includes index. |
| 505 ## - FORMATTED CONTENTS NOTE | |
| Contents | Preface<br/>Prologue: The Exponential Function<br/>Chapter 1: Abstract Integration<br/>Set-theoretic notations and terminology<br/>The concept of measurability<br/>Simple functions<br/>Elementary properties of measures<br/>Arithmetic in [0, ∞]<br/>Integration of positive functions<br/>Integration of complex functions<br/>The role played by sets of measure zero<br/>Exercises<br/>Chapter 2: Positive Borel Measures<br/>Vector spaces<br/>Topological preliminaries<br/>The Riesz representation theorem<br/>Regularity properties of Borel measures<br/>Lebesgue measure<br/>Continuity properties of measurable functions<br/>Exercises<br/>Chapter 3: Lp-Spaces<br/>Convex functions and inequalities<br/>The Lp-spaces<br/>Approximation by continuous functions<br/>Exercises<br/>Chapter 4: Elementary Hilbert Space Theory<br/>Inner products and linear functionals<br/>Orthonormal sets<br/>Trigonometric series<br/>Exercises<br/>Chapter 5: Examples of Banach Space Techniques<br/>Banach spaces<br/>Consequences of Baire's theorem<br/>Fourier series of continuous functions<br/>Fourier coefficients of L1-functions<br/>The Hahn-Banach theorem<br/>An abstract approach to the Poisson integral<br/>Exercises<br/>Chapter 6: Complex Measures<br/>Total variation<br/>Absolute continuity<br/>Consequences of the Radon-Nikodym theorem<br/>Bounded linear functionals on Lp<br/>The Riesz representation theorem<br/>Exercises<br/>Chapter 7: Differentiation<br/>Derivatives of measures<br/>The fundamental theorem of Calculus<br/>Differentiable transformations<br/>Exercises<br/>Chapter 8: Integration on Product Spaces<br/>Measurability on cartesian products<br/>Product measures<br/>The Fubini theorem<br/>Completion of product measures<br/>Convolutions<br/>Distribution functions<br/>Exercises<br/>Chapter 9: Fourier Transforms<br/>Formal properties<br/>The inversion theorem<br/>The Plancherel theorem<br/>The Banach algebra L1<br/>Exercises<br/>Chapter 10: Elementary Properties of Holomorphic Functions<br/>Complex differentiation<br/>Integration over paths<br/>The local Cauchy theorem<br/>The power series representation<br/>The open mapping theorem<br/>The global Cauchy theorem<br/>The calculus of residues<br/>Exercises<br/>Chapter 11: Harmonic Functions<br/>The Cauchy-Riemann equations<br/>The Poisson integral<br/>The mean value property<br/>Boundary behavior of Poisson integrals<br/>Representation theorems<br/>Exercises<br/>Chapter 12: The Maximum Modulus Principle<br/>Introduction<br/>The Schwarz lemma<br/>The Phragmen-Lindelöf method<br/>An interpolation theorem<br/>A converse of the maximum modulus theorem<br/>Exercises<br/>Chapter 13: Approximation by Rational Functions<br/>Preparation<br/>Runge's theorem<br/>The Mittag-Leffler theorem<br/>Simply connected regions<br/>Exercises<br/>Chapter 14: Conformal Mapping<br/>Preservation of angles<br/>Linear fractional transformations<br/>Normal families<br/>The Riemann mapping theorem<br/>The class L<br/>Continuity at the boundary<br/>Conformal mapping of an annulus<br/>Exercises<br/>Chapter 15: Zeros of Holomorphic Functions<br/>Infinite Products<br/>The Weierstrass factorization theorem<br/>An interpolation problem<br/>Jensen's formula<br/>Blaschke products<br/>The Müntz-Szas theorem<br/>Exercises<br/>Chapter 16: Analytic Continuation<br/>Regular points and singular points<br/>Continuation along curves<br/>The monodromy theorem<br/>Construction of a modular function<br/>The Picard theorem<br/>Exercises<br/>Chapter 17: Hp-Spaces<br/>Subharmonic functions<br/>The spaces Hp and N<br/>The theorem of F. and M. Riesz<br/>Factorization theorems<br/>The shift operator<br/>Conjugate functions<br/>Exercises<br/>Chapter 18: Elementary Theory of Banach Algebras<br/>Introduction<br/>The invertible elements<br/>Ideals and homomorphisms<br/>Applications<br/>Exercises<br/>Chapter 19: Holomorphic Fourier Transforms<br/>Introduction<br/>Two theorems of Paley and Wiener<br/>Quasi-analytic classes<br/>The Denjoy-Carleman theorem<br/>Exercises<br/>Chapter 20: Uniform Approximation by Polynomials<br/>Introduction<br/>Some lemmas<br/>Mergelyan's theorem<br/>Exercises<br/>Appendix: Hausdorff's Maximality Theorem<br/>Notes and Comments<br/>Bibliography<br/>List of Special Symbols<br/>Index |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc | This is an advanced text for the one- or two-semester course in analysis taught primarily to math, science, computer science, and electrical engineering majors at the junior, senior or graduate level. The basic techniques and theorems of analysis are presented in such a way that the intimate connections between its various branches are strongly emphasized. The traditionally separate subjects of 'real analysis' and 'complex analysis' are thus united in one volume. Some of the basic ideas from functional analysis are also included. This is the only book to take this unique approach. The third edition includes a new chapter on differentiation. Proofs of theorems presented in the book are concise and complete and many challenging exercises appear at the end of each chapter. The book is arranged so that each chapter builds upon the other, giving students a gradual understanding of the subject.<br/><br/>This text is part of the Walter Rudin Student Series in Advanced Mathematics. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Mathematical analysis. |
| 690 ## - LOCAL SUBJECT ADDED ENTRY--TOPICAL TERM (OCLC, RLIN) | |
| Department Name | Mathematics |
| 856 ## - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | <a href="https://www.mheducation.com/highered/product/real-complex-analysis-rudin/M9780070542341.html#overview">https://www.mheducation.com/highered/product/real-complex-analysis-rudin/M9780070542341.html#overview</a> |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) | |
| Source of classification or shelving scheme | Dewey Decimal Classification |
| Koha item type | Project book |
| 100 10 - MAIN ENTRY--PERSONAL NAME | |
| Dates associated with a name | , 1921- |
| 504 ## - BIBLIOGRAPHY, ETC. NOTE | |
| Bibliography, etc | Bibliography: p. 405-406. |
| 740 01 - ADDED ENTRY--UNCONTROLLED RELATED/ANALYTICAL TITLE | |
| Uncontrolled related/analytical title | Real & complex analysis. |
| Withdrawn status | Lost status | Source of classification or shelving scheme | Damaged status | Not for loan | Home library | Location | Date of Cataloging | Total Checkouts | Full call number | Barcode | Checked out | Date last seen | Date checked out | Price effective from | Koha item type | Collection code | Shelving location |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Dewey Decimal Classification | CUTN Central Library | CUTN Central Library | 14/11/2023 | 1 | 515 RUD | 48871 | 31/01/2024 | 03/01/2024 | 03/01/2024 | 14/11/2023 | Project book | ||||||
| Dewey Decimal Classification | CUTN Central Library | CUTN Central Library | 05/11/2024 | 515 RUD | 49434 | 05/11/2024 | 05/11/2024 | General Books | Non-fiction | Sciences |