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Undergraduate analysis : a working textbook /
An innovative self-contained Analysis textbook for undergraduates, that takes advantage of proven successful educational techniques.
| Clasificación: | Libro Electrónico |
|---|---|
| Autores principales: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Oxford, United Kingdom :
Oxford University Press,
2018.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 2.9 POSTSCRIPT: to infinity2.10 Important note on 'elementary functions'; 3 Interlude: different kinds of numbers; 3.1 Sets; 3.2 Intervals, max and min, sup and inf; 3.3 Denseness; 4 Up and down
- increasing and decreasing sequences; 4.1 Monotonic bounded sequences must converge; 4.2 Induction: infinite returns for finite effort; 4.3 Recursively defined sequences; 4.4 POSTSCRIPT: The epsilontics game
- the 'fifth factor of difficulty'; 5 Sampling a sequence
- subsequences; 5.1 Introduction; 5.2 Subsequences; 5.3 Bolzano-Weierstrass: the overcrowded interval
- 6 Special (or specially awkward) examples6.1 Introduction; 6.2 Important examples of convergence; 7 Endless sums
- a first look at series; 7.1 Introduction; 7.2 Definition and easy results; 7.3 Big series, small series: comparison tests; 7.4 The root test and the ratio test; 8 Continuous functions
- the domain thinks that the graph is unbroken; 8.1 Introduction; 8.2 An informal view of continuity; 8.3 Continuity at a point; 8.4 Continuity on a set; 8.5 Key theorems on continuity; 8.6 Continuity of the inverse; 9 Limit of a function; 9.1 Introduction; 9.2 Limit of a function at a point
- 10 Epsilontics and functions10.1 The epsilontic view of function limits; 10.2 The epsilontic view of continuity; 10.3 One-sided limits; 11 Infinity and function limits; 11.1 Limit of a function as x tends to infinity or minus infinity; 11.2 Functions tending to infinity or minus infinity; 12 Differentiation
- the slope of the graph; 12.1 Introduction; 12.2 The derivative; 12.3 Up and down, maximum and minimum: for differentiable functions; 12.4 Higher derivatives; 12.5 Alternative proof of the chain rule; 13 The Cauchy condition
- sequences whose terms pack tightly together
- 13.1 Cauchy equals convergent14 More about series; 14.1 Absolute convergence; 14.2 The 'robustness' of absolutely convergent series; 14.3 Power series; 15 Uniform continuity
- continuity's global cousin; 15.1 Introduction; 15.2 Uniformly continuous functions; 15.3 The bounded derivative test; 16 Differentiation
- mean value theorems, power series; 16.1 Introduction; 16.2 Cauchy and l'Hôpital; 16.3 Taylor series; 16.4 Differentiating a power series; 17 Riemann integration
- area under a graph; 17.1 Introduction
- 17.2 Riemann integrability
- how closely can rectangles approximate areas under graphs?