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It provides a transition from elementary calculus to advanced courses in real and complex function theory and introduces the reader to some of the abstract thinking that pervades modern analysis.
Table of Contents
1. The Real and Complex Number Systems. 2. Some Basic Notions of Set Theory. 3. Elements of Point Set Topology. 4. Limits and Continuity. 5. Derivatives. 6. Functions of Bounded Variation and Rectifiable Curves. 7. The Riemann-Stieltjes Integral. 8. Infinite Series and Infinite Products. 9. Sequences of Functions. 10. The Lebesgue Integral. 11. Fourier Series and Fourier Integrals. 12. Multivariable Differential Calculus. 13. Implicit Functions and Extremum Problems. 14. Multiple Riemann Integrals. 15. Multiple Lebesgue Integrals. 16. Cauchy's Theorem and the Residue Calculus.