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Further exercises; Chapter 9. Mean Values and Taylor Series; 9.1 The Mean Value Theorem; 9.2 Tests for extreme points; 9.3 L'Hôpital's Rules and the calculation of limits; 9.4 Differentiation of power series; 9.5 Taylor's Theorem and series expansions; Summary; Further exercises; Cha...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Oxford :
Elsevier,
1996.
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| Colección: | Modular mathematics series.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Front Cover; Analysis; Copyright Page; Table of Contents; Series Preface; Preface; Acknowledgements; Chapter 1. Introduction: Why We Study Analysis; 1.1 What the computer cannot see ... ; 1.2 From counting to complex numbers; 1.3 From infinitesimals to limits; Chapter 2. Convergent Sequences and Series; 2.1 Convergence and summation; 2.2 Algebraic and order properties of limits; Summary; Further exercises; Chapter 3. Completenessand Convergence; 3.1 Completeness and sequences; 3.2 Completeness and series; 3.3 Alternating series; 3.4 Absolute and conditional convergence of series; Summary.
- Further exercisesChapter 4. Functions Definedby Power Series; 4.1 Polynomials
- and what Euler did with them!; 4.2 Multiplying power series: Cauchy products; 4.3 The radius of convergence of a power series; 4.4 The elementary transcendental functions; Summary; Further exercises; Chapter 5. Functions and Limits; 5.1 Historical interlude: curves, graphs and functions; 5.2 The modern concept of function: ordered pairs, domainand range; 5.3 Combining real functions; 5.4 Limits of real functions
- what Cauchy meant!; Summary; Further exercises; Chapter 6. Continuous Functions; 6.1 Limits that fit.
- 6.2 Limits that do not fit: types of discontinuity6.3 General power functions; 6.4 Continuity of power series; Summary; Further exercises; Chapter 7. Continuity on Intervals; 7.1 From interval to interval; 7.2 Applications: fixed points, roots and iteration; 7.3 Reaching the maximum: the Boundedness Theorem; 7.4 Uniform continuity
- what Cauchy meant?; Summary; Further exercises; Chapter 8. Differentiable Real Functions; 8.1 Tangents: prime and ultimate ratios; 8.2 The derivative as a limit; 8.3 Differentiation and continuity; 8.4 Combining derivatives; 8.5 Extreme points and curve sketching.
- 11.1 The Fundamental Theorem of the Calculus11.2 Integration by parts and change of variable; 11.3 Improper integrals; 11.4 Convergent integrals and convergent series; Summary; Further exercises; Chapter 12. What Next? Extensions and Developments; 12.1 Generalizations of completeness; 12.2 Approximation of functions; 12.3 Integrals of real functions: yet more completeness; Appendix A: Program Listings; A.I Sequences program; A.2 Another sequence program; A.3 Taylor series; A.4 Newton's method in one dimension; Solutions to exercises; Index.