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An introduction to mathematical analysis /
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Oxford :
Pergamon Press,
1963.
|
| Colección: | International series in pure and applied mathematics ;
v. 43. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Front Cover ; An Introduction to Mathematical Analysis ; Copyright Page ; Table of Contents ; Dedication ; PREFACE; LIST OF SYMBOLS AND NOTATIONS; CHAPTER 1. FUNDAMENTAL IDEAS AND ASSUMPTIONS ; 1. INTRODUCTION; 2. ASSUMPTIONS RELATING TO THE FIELD OPERATIONS ; 3. ASSUMPTIONS RELATING TO THE ORDERING OF THE REAL NUMBERS ; 4. MATHEMATICAL INDUCTION; 5. UPPER AND LOWER BOUNDS OF SETS OF REAL NUMBERS; 6. FUNCTIONS; CHAPTER 2. LIMITS AND CONTINUITY ; 7. LIMITS OF REAL FUNCTIONS DEFINED ON THE POSITIVE INTEGERS ; 8. LIMITS OF REAL FUNCTIONS OF A REAL VARIABLE x AS x TENDS TO INFINITY.
- 9. ELEMENTARY TOPOLOGICAL IDEAS10. LIMITS OF REAL FUNCTIONS AT FINITE POINTS; 11. CONTINUITY; 12. INVERSE FUNCTIONS AND FRACTIONAL INDICES; CHAPTER 3. DIFFERENTIABILITY ; 13. DERIVATIVES; 14. GENERAL THEOREMS CONCERNING REALFUNCTIONS; 15. MAXIMA, MINIMA AND CONVEXITY; 16. COMPLEX NUMBERS AND FUNCTIONS; CHAPTER 4. INFINITE SERIES ; 17. ELEMENTARY PROPERTIES OF INFINITE SERIES; 18. SERIES WITH NON-NEGATIVE TERMS; 19. ABSOLUTE AND CONDITIONAL CONVERGENCE; 20. THE DECIMAL NOTATION FOR REAL NUMBERS; CHAPTER 5. FUNCTIONS DEFINED BY POWER SERIES ; 21. GENERAL THEORY OF POWER SERIES.
- 22. REAL POWER SERIES23. THE EXPONENTIAL AND LOGARITHMICFUNCTIONS; 24. THE TRIGONOMETRIC FUNCTIONS; 25. THE HYPERBOLIC FUNCTIONS; 26. COMPLEX INDICES; CHAPTER 6. INTEGRATION ; 27. THE INDEFINITE INTEGRAL; 28. INTERVAL FUNCTIONS AND FUNCTIONSOF BOUNDED VARIATION; 29. THE RIEMANN-STIELTJES INTEGRAL ; 30. THE RIEMANN INTEGRAL; 31. CURVES; 32. AREA; CHAPTER 7. CONVERGENCE AND UNIFORMITY; 33. UPPER AND LOWER LIMITS AND THEIR APPLICATIONS ; 34. FURTHER CONVERGENCE TESTS FOR INFINITESERIES; 35. UNIFORM CONVERGENCE; 36. IMPROPER INTEGRALS; 37. DOUBLE SERIES; 38. INFINITE PRODUCTS.