This text is a single variable real analysis text, designed for the one-year course at the junior, senior, or beginning graduate level. It provides a rigorous and comprehensive treatment of the theoretical concepts of analysis. The book contains most of the topics covered in a text of this nature, but it also includes many topics not normally encountered in comparable texts. These include the Riemann-Stieltjes integral, the Lebesgue integral, Fourier series, the Weiestrass approximation theorem, and an introduction to normal linear spaces.
KEY TOPICS: The Real Number System; Sequence Of Real Numbers; Structure Of Point Sets; Limits And Continuity; Differentiation; The Riemann And Riemann-Stieltjes Integral; Series of Real Numbers; Sequences And Series Of Functions; Orthogonal Functions And Fourier Series; Lebesgue Measure And Integration; Logic and Proofs; Propositions and Connectives
MARKET: For all readers interested in real analysis.
Table of contents
1. The Real Number System.
2. Sequence Of Real Numbers.
3. Structure Of Point Sets.
4. Limits And Continuity.
6. The Riemann And Riemann-Stieltjes Integral.
7. Series of Real Numbers.
8. Sequences And Series Of Functions.
9. Orthogonal Functions And Fourier Series.
10. Lebesgue Measure And Integration.
Appendix: Logic and Proofs.
Propositions and Connectives.
Hints and Solutions to Selected Exercises.
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