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A first course in analysis /
| Autor principal: | |
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| Formato: | Libro |
| Lenguaje: | English |
| Publicado: |
New York Berlin :
Springer-Verlag,
1994, 1994.
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| Colección: | Undergraduate texts in mathematics
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| Materias: |
Tabla de Contenidos:
- 4. The elementary functions. 5. Uniformity. The Heine-Borel theorem. 6. Uniform convergence. A nowhere differentiable continuous function. 7. The Weierstrass approximation theorem
- Appendix. A Space-filling continuous curve
- Ch. 4. Differentiation. 1. Differential and derivative. Tangent line. 2. The foundations of differentiation. 3. Curve sketching. The mean-value theorem. 4. Taylor's theorem. 5. Functions defined Implicitly
- Ch. 5. Integration. 1. Definitions. Darboux theorem. 2. Foundations of integral calculus. The fundamental theorem of calculus. 3. The nature of integrability. Lebesgue's theorem. 4. Improper integral. 5. Arclength. Bounded variation
- A word about the Stieltjes integral and measure theory
- Ch. 6. Infinite series. 1. The vibrating string. 2. Convergence: general considerations. 3. Convergence: series of positive terms. 4. Computation with series. 5. Power series. 6. Fourier series.