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An introduction to real analysis / / Derek G. Ball
An introduction to real analysis / / Derek G. Ball
Autore Ball Derek <1942->
Edizione [First edition.]
Pubbl/distr/stampa Oxford, England : , : Pergamon Press, , 1973
Descrizione fisica 1 online resource (324 p.)
Disciplina 515
Collana Commonwealth and International Library. Mathematical Topics
Soggetto topico Mathematical analysis
Numbers, Real
ISBN 1-4831-5896-9
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Front Cover; An Introduction to Real Analysis; Copyright Page; Table of Contents; PREFACE; INTRODUCTION. THE PURPOSE OF REAL ANALYSIS; CHAPTER 1. SETS, RELATIONS, AND FUNCTIONS; 1.1. Sets; 1.2. Relations and Functions; CHAPTER 2. NUMBERS; 2.1. Natural numbers; 2.2. Integers; 2.3. Rationals; 2.4. Real Numbers; 2.5. Irrationals; 2.6. Appendix; CHAPTER 3. SEQUENCES; 3.1. Introduction; 3.2. Limits of sequences; 3.3. Elementary theorems about sequences; 3.4. Behaviour of monotonie sequences; 3.5. Sequences defined by recurrence relations; 3.6. More sequences and their limits
3.7. Upper and lower limitsCHAPTER 4. SERIES; 4.1. Introduction; 4.2. Convergence of a series; 4.3. More series, convergent and divergent; 4.4 The comparison test; 4.5. Decimal representation; 4.6. Absolute convergence; 4.7. Conditional convergence; 4.8. Rearrangement of series; 4.9. Multiplication of series; CHAPTER 5. FUNCTIONS OF A REAL VARIABLE; 5.1. Introduction; 5.2. Limits; 5.3. Properties of limits; 5.4. Continuity; 5.5. The place of pathological functions in real analysis; 5.6. The nature of discontinuities; 5.7. Properties of continuous functions; CHAPTER 6. THE DERIVATIVE
6.1. Derivatives and their evaluation6.2. Rolle's theorem and the nature of the derivative; 6.3. Mean value theorems; 6.4. Applications of derivatives; 6.5. Taylor series; CHAPTER 7. SOME IMPORTANT FUNCTIONS AND EXPANSIONS; 7.1. Power series; 7.2. The exponential function; 7.3. Trigonometric functions; 7.4. Logarithmic functions; 7.5. Infinite products; 7.6. The binomial theorem; CHAPTER 8. THE RIEMANN INTEGRAL; 8.1. Introduction; 8.2. The Riemann integral; 8.3. Integrability of monotonic functions; 8.4. Continuous functions and the Riemann integral
8.5. Further applications of the fundamental theorem8.6. Alternative approach to the logarithmic function; 8.7. Infinite and improper integrals; 8.8 Volumes of revolution; ANSWERS AND HINTS; INDEX
Record Nr. UNINA-9910786641603321
Ball Derek <1942->  
Oxford, England : , : Pergamon Press, , 1973
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
An introduction to real analysis / / Derek G. Ball
An introduction to real analysis / / Derek G. Ball
Autore Ball Derek <1942->
Edizione [First edition.]
Pubbl/distr/stampa Oxford, England : , : Pergamon Press, , 1973
Descrizione fisica 1 online resource (324 p.)
Disciplina 515
Collana Commonwealth and International Library. Mathematical Topics
Soggetto topico Mathematical analysis
Numbers, Real
ISBN 1-4831-5896-9
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Front Cover; An Introduction to Real Analysis; Copyright Page; Table of Contents; PREFACE; INTRODUCTION. THE PURPOSE OF REAL ANALYSIS; CHAPTER 1. SETS, RELATIONS, AND FUNCTIONS; 1.1. Sets; 1.2. Relations and Functions; CHAPTER 2. NUMBERS; 2.1. Natural numbers; 2.2. Integers; 2.3. Rationals; 2.4. Real Numbers; 2.5. Irrationals; 2.6. Appendix; CHAPTER 3. SEQUENCES; 3.1. Introduction; 3.2. Limits of sequences; 3.3. Elementary theorems about sequences; 3.4. Behaviour of monotonie sequences; 3.5. Sequences defined by recurrence relations; 3.6. More sequences and their limits
3.7. Upper and lower limitsCHAPTER 4. SERIES; 4.1. Introduction; 4.2. Convergence of a series; 4.3. More series, convergent and divergent; 4.4 The comparison test; 4.5. Decimal representation; 4.6. Absolute convergence; 4.7. Conditional convergence; 4.8. Rearrangement of series; 4.9. Multiplication of series; CHAPTER 5. FUNCTIONS OF A REAL VARIABLE; 5.1. Introduction; 5.2. Limits; 5.3. Properties of limits; 5.4. Continuity; 5.5. The place of pathological functions in real analysis; 5.6. The nature of discontinuities; 5.7. Properties of continuous functions; CHAPTER 6. THE DERIVATIVE
6.1. Derivatives and their evaluation6.2. Rolle's theorem and the nature of the derivative; 6.3. Mean value theorems; 6.4. Applications of derivatives; 6.5. Taylor series; CHAPTER 7. SOME IMPORTANT FUNCTIONS AND EXPANSIONS; 7.1. Power series; 7.2. The exponential function; 7.3. Trigonometric functions; 7.4. Logarithmic functions; 7.5. Infinite products; 7.6. The binomial theorem; CHAPTER 8. THE RIEMANN INTEGRAL; 8.1. Introduction; 8.2. The Riemann integral; 8.3. Integrability of monotonic functions; 8.4. Continuous functions and the Riemann integral
8.5. Further applications of the fundamental theorem8.6. Alternative approach to the logarithmic function; 8.7. Infinite and improper integrals; 8.8 Volumes of revolution; ANSWERS AND HINTS; INDEX
Record Nr. UNINA-9910824454303321
Ball Derek <1942->  
Oxford, England : , : Pergamon Press, , 1973
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui