Tabla de Contenidos:
  • Introduction: Assumptions and Notations
  • 1. Sets and functions
  • 2. Sequences of real numbers
  • 3. Series of real numbers
  • 4. Limits and metric spaces
  • 5. Continuous functions on metric spaces
  • 6. Connectedness, completeness, and compactness
  • 7. Calculus
  • 8. The elementary functions. Taylor series
  • 9. Sequences and series of functions
  • 10. Three famous theorems
  • 11. The Lebesgue integral
  • 12. Fourier series
  • Appendix: The algebraic and order axioms for the real numbers
  • Special Symbols
  • Index