Introduction to Real Analysis

,

Wysyłka: Niedostępna
Sugerowana cena detaliczna 668,90 PLN
Nasza cena: 631,10 PLN
Oszczędzasz 5%
Dodaj do Schowka
Zaloguj się
Przypomnij hasło
×
×
Paypo
Oferujemy szeroki asortyment - ponad 120 tys. produktów
Dysponujemy solidną wiedzą - działamy już 11 lat
Dbamy o wybór najcenniejszych tytułów

Opis: Introduction to Real Analysis - Donald R. Sherbert, Robert G. Bartle

This text provides the fundamental concepts and techniques of real analysis for students in all of these areas. It helps one develop the ability to think deductively, analyse mathematical situations and extend ideas to a new context. Like the first three editions, this edition maintains the same spirit and user-friendly approach with addition examples and expansion on Logical Operations and Set Theory. There is also content revision in the following areas: introducing point-set topology before discussing continuity, including a more thorough discussion of limsup and limimf, covering series directly following sequences, adding coverage of Lebesgue Integral and the construction of the reals, and drawing student attention to possible applications wherever possible.CHAPTER 1 PRELIMINARIES. 1.1 Sets and Functions. 1.2 Mathematical Induction. 1.3 Finite and Infinite Sets. CHAPTER 2 THE REAL NUMBERS. 2.1 The Algebraic and Order Properties of R. 2.2 Absolute Value and the Real Line. 2.3 The Completeness Property of R. 2.4 Applications of the Supremum Property. 2.5 Intervals. CHAPTER 3 SEQUENCES AND SERIES. 3.1 Sequences and Their Limits. 3.2 Limit Theorems. 3.3 Monotone Sequences. 3.4 Subsequences and the Bolzano-Weierstrass Theorem. 3.5 The Cauchy Criterion. 3.6 Properly Divergent Sequences. 3.7 Introduction to Infinite Series. CHAPTER 4 LIMITS. 4.1 Limits of Functions. 4.2 Limit Theorems. 4.3 Some Extensions of the Limit Concept. CHAPTER 5 CONTINUOUS FUNCTIONS. 5.1 Continuous Functions. 5.2 Combinations of Continuous Functions. 5.3 Continuous Functions on Intervals. 5.4 Uniform Continuity. 5.5 Continuity and Gauges. 5.6 Monotone and Inverse Functions. CHAPTER 6 DIFFERENTIATION. 6.1 The Derivative. 6.2 The Mean Value Theorem. 6.3 L'Hospital's Rules. 6.4 Taylor's Theorem. CHAPTER 7 THE RIEMANN INTEGRAL. 7.1 Riemann Integral. 7.2 Riemann Integrable Functions. 7.3 The Fundamental Theorem. 7.4 The Darboux Integral. 7.5 Approximate Integration. CHAPTER 8 SEQUENCES OF FUNCTIONS. 8.1 Pointwise and Uniform Convergence. 8.2 Interchange of Limits. 8.3 The Exponential and Logarithmic Functions. 8.4 The Trigonometric Functions. CHAPTER 9 INFINITE SERIES. 9.1 Absolute Convergence. 9.2 Tests for Absolute Convergence. 9.3 Tests for Nonabsolute Convergence. 9.4 Series of Functions. CHAPTER 10 THE GENERALIZED RIEMANN INTEGRAL. 10.1 Definition and Main Properties. 10.2 Improper and Lebesgue Integrals. 10.3 Infinite Intervals. 10.4 Convergence Theorems. CHAPTER 11 A GLIMPSE INTO TOPOLOGY. 11.1 Open and Closed Sets in R. 11.2 Compact Sets. 11.3 Continuous Functions. 11.4 Metric Spaces. APPENDIX A LOGIC AND PROOFS. APPENDIX B FINITE AND COUNTABLE SETS. APPENDIX C THE RIEMANN AND LEBESGUE CRITERIA. APPENDIX D APPROXIMATE INTEGRATION. APPENDIX E TWO EXAMPLES. REFERENCES. PHOTO CREDITS. HINTS FOR SELECTED EXERCISES. INDEX.


Szczegóły: Introduction to Real Analysis - Donald R. Sherbert, Robert G. Bartle

Tytuł: Introduction to Real Analysis
Autor: Donald R. Sherbert, Robert G. Bartle
Producent: John Wiley
ISBN: 9780471433316
Rok produkcji: 2011
Ilość stron: 402
Oprawa: Twarda
Waga: 0.76 kg


Recenzje: Introduction to Real Analysis - Donald R. Sherbert, Robert G. Bartle

Zaloguj się
Przypomnij hasło
×
×

Introduction to Real Analysis

,

This text provides the fundamental concepts and techniques of real analysis for students in all of these areas. It helps one develop the ability to think deductively, analyse mathematical situations and extend ideas to a new context. Like the first three editions, this edition maintains the same spirit and user-friendly approach with addition examples and expansion on Logical Operations and Set Theory. There is also content revision in the following areas: introducing point-set topology before discussing continuity, including a more thorough discussion of limsup and limimf, covering series directly following sequences, adding coverage of Lebesgue Integral and the construction of the reals, and drawing student attention to possible applications wherever possible.CHAPTER 1 PRELIMINARIES. 1.1 Sets and Functions. 1.2 Mathematical Induction. 1.3 Finite and Infinite Sets. CHAPTER 2 THE REAL NUMBERS. 2.1 The Algebraic and Order Properties of R. 2.2 Absolute Value and the Real Line. 2.3 The Completeness Property of R. 2.4 Applications of the Supremum Property. 2.5 Intervals. CHAPTER 3 SEQUENCES AND SERIES. 3.1 Sequences and Their Limits. 3.2 Limit Theorems. 3.3 Monotone Sequences. 3.4 Subsequences and the Bolzano-Weierstrass Theorem. 3.5 The Cauchy Criterion. 3.6 Properly Divergent Sequences. 3.7 Introduction to Infinite Series. CHAPTER 4 LIMITS. 4.1 Limits of Functions. 4.2 Limit Theorems. 4.3 Some Extensions of the Limit Concept. CHAPTER 5 CONTINUOUS FUNCTIONS. 5.1 Continuous Functions. 5.2 Combinations of Continuous Functions. 5.3 Continuous Functions on Intervals. 5.4 Uniform Continuity. 5.5 Continuity and Gauges. 5.6 Monotone and Inverse Functions. CHAPTER 6 DIFFERENTIATION. 6.1 The Derivative. 6.2 The Mean Value Theorem. 6.3 L'Hospital's Rules. 6.4 Taylor's Theorem. CHAPTER 7 THE RIEMANN INTEGRAL. 7.1 Riemann Integral. 7.2 Riemann Integrable Functions. 7.3 The Fundamental Theorem. 7.4 The Darboux Integral. 7.5 Approximate Integration. CHAPTER 8 SEQUENCES OF FUNCTIONS. 8.1 Pointwise and Uniform Convergence. 8.2 Interchange of Limits. 8.3 The Exponential and Logarithmic Functions. 8.4 The Trigonometric Functions. CHAPTER 9 INFINITE SERIES. 9.1 Absolute Convergence. 9.2 Tests for Absolute Convergence. 9.3 Tests for Nonabsolute Convergence. 9.4 Series of Functions. CHAPTER 10 THE GENERALIZED RIEMANN INTEGRAL. 10.1 Definition and Main Properties. 10.2 Improper and Lebesgue Integrals. 10.3 Infinite Intervals. 10.4 Convergence Theorems. CHAPTER 11 A GLIMPSE INTO TOPOLOGY. 11.1 Open and Closed Sets in R. 11.2 Compact Sets. 11.3 Continuous Functions. 11.4 Metric Spaces. APPENDIX A LOGIC AND PROOFS. APPENDIX B FINITE AND COUNTABLE SETS. APPENDIX C THE RIEMANN AND LEBESGUE CRITERIA. APPENDIX D APPROXIMATE INTEGRATION. APPENDIX E TWO EXAMPLES. REFERENCES. PHOTO CREDITS. HINTS FOR SELECTED EXERCISES. INDEX.

Powiadom o dostępności
Podaj swój e-mail a zostaniesz poinformowany jak tylko pozycja będzie dostępna.
×
Cena 668,90 PLN
Nasza cena 631,10 PLN
Oszczędzasz 5%
Wysyłka: Niedostępna
Dodaj do Schowka
Zaloguj się
Przypomnij hasło
×
×

Paypo

Szczegóły: Introduction to Real Analysis - Donald R. Sherbert, Robert G. Bartle

Tytuł: Introduction to Real Analysis
Autor: Donald R. Sherbert, Robert G. Bartle
Producent: John Wiley
ISBN: 9780471433316
Rok produkcji: 2011
Ilość stron: 402
Oprawa: Twarda
Waga: 0.76 kg


Recenzje: Introduction to Real Analysis - Donald R. Sherbert, Robert G. Bartle

Zaloguj się
Przypomnij hasło
×
×

Klienci, którzy kupili oglądany produkt kupili także:


Zaloguj się
Przypomnij hasło
×
×
Dodane do koszyka
×