Understanding analysis /

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A textbook for an elementary, one-semester course in a mathematically rigorous approach to the study of functions of a real variable. Focuses on the questions that make the subject most interesting to new students, such as whether derivatives are integrable or continuous. Makes topics accessible by...

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Detalles Bibliográficos
Clasificación:QA300 A2.36
Autor principal: Abbott, Stephen, 1964- (autor)
Formato: Libro
Idioma:Inglés
Publicado: New York : Springer, 2001.
Colección:Undergraduate texts in mathematics
Temas:
Mathematical analysis
Análisis matemático

MARC

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050 4 |a QA300  |b A2.36 
082 0 0 |a 515 
090 |a QA300  |b A2.36 
100 1 |a Abbott, Stephen,  |d 1964-,  |e autor 
245 1 0 |a Understanding analysis /  |c Stephen Abbott. 
264 1 |a New York :  |b Springer,  |c 2001. 
300 |a xii, 257 páginas :  |b ilustraciones ;  |c 25 cm. 
336 |a texto  |b txt  |2 rdacontent 
337 |a sin medio  |b n  |2 rdamedia 
338 |a volumen  |b nc  |2 rdacarrier 
490 1 |a Undergraduate texts in mathematics 
504 |a Incluye referencias bibliográficas: (páginas 251-252). 
505 2 0 |g 1.  |t The Real Numbers. --  |g 1.1.  |t Discussion: The Irrationality of [square root of]2. --  |g 1.2.  |t Some Preliminaries. --  |g 1.3.  |t The Axiom of Completeness. --  |g 1.4.  |t Consequences of Completeness. --  |g 1.5.  |t Cantor's Theorem. --  |g 2.  |t Sequences and Series. --  |g 2.1.  |t Discussion: Rearrangements of Infinite Series. --  |g 2.2.  |t The Limit of a Sequence. --  |g 2.3.  |t The Algebraic and Order Limit Theorems. --  |g 2.4.  |t The Monotone Convergence Theorem and a First Look at Infinite Series. --  |g 2.5.  |t Subsequences and the Bolzano-Weierstrass Theorem. --  |g 2.6.  |t The Cauchy Criterion. --  |g 2.7.  |t Properties of Infinite Series. --  |g 2.8.  |t Double Summations and Products of Infinite Series. --  |g 3.  |t Basic Topology of R. --  |g 3.1.  |t Discussion: The Cantor Set. --  |g 3.2.  |t Open and Closed Sets. --  |g 3.3.  |t Compact Sets. --  |g 3.4.  |t Perfect Sets and Connected Sets. --  |g 3.5.  |t Baire's Theorem. --  |g 4.  |t Functional Limits and Continuity. --  |g 4.1.  |t Discussion: Examples of Dirichlet and Thomae. --  |g 4.2.  |t Functional Limits. --  |g 4.3.  |t Combinations of Continuous Functions. --  |g 4.4.  |t Continuous Functions on Compact Sets. --  |g 4.5.  |t The Intermediate Value Theorem. --  |g 4.6.  |t Sets of Discontinuity. --  |g 5.  |t The Derivative. --  |g 5.1.  |t Discussion: Are Derivatives Continuous?. --  |g 5.2.  |t Derivatives and the Intermediate Value Property. --  |g 5.3.  |t The Mean Value Theorem. --  |g 5.4.  |t A Continuous Nowhere-Differentiable Function. 
520 0 |a A textbook for an elementary, one-semester course in a mathematically rigorous approach to the study of functions of a real variable. Focuses on the questions that make the subject most interesting to new students, such as whether derivatives are integrable or continuous. Makes topics accessible by answering these questions using mathematics. DLC: Mathematical analysis. *** This book outlines an elementary, one-semester course which exposes students to both the process of rigor, and the rewards inherent in taking an axiomatic approach to the study of functions of a real variable. The aim of a course in real analysis should be to challenge and improve mathematical intuition rather than to verify it. The philosophy of this book is to focus attention on questions which give analysis its inherent fascination. 
650 0 |a Mathematical analysis 
650 4 |a Análisis matemático 
830 0 |a Undergraduate texts in mathematics 
905 |a LIBROS 
938 |a Comunidad  |c CBI 
938 |a Dr. Dr. Carlos Signoret Pendiente ;  |b Ecuaciones diferenciales  |n Octubre 27, 2003.  |c Solic. Difusión Científica  |n Estruc prog. 126020192; 
949 |a Biblioteca UAM Iztapalapa  |b Colección General  |c QA300 A2.36 

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