- Bases most of the various limit concepts on sequential limits, which is done first
- Defines function limits by first developing the notion of continuity (with a sequential limit characterization)
- Contains a thorough development of the Riemann integral, improper integrals (including sections on the gamma function and the Laplace transform), and the Stieltjes integral
- Presents general metric space topology in juxtaposition with Euclidean spaces to ease the transition from the concrete setting to the abstract
New to This Edition
- Contains new Exercises throughout
- Provides a simple definition of subsequence
- Contains more information on function limits and L'Hospital's Rule
- Provides clearer proofs about rational numbers and the integrals of Riemann and Stieltjes
- Presents an appendix lists all mathematicians named in the text
- Gives a glossary of symbols
Ordering of the Real Numbers.
Completeness of the Real Numbers.
Consequences of Continuity.
The Riemann Integral.
The Riemann-Stieltjes Integral.
Metric Spaces and Euclidean Spaces.
Differential Calculus in Euclidean Spaces.
Area and Integration in E².
Appendix A. Mathematical Induction.
Appendix B. Countable and Uncountable Sets.
Appendix C. Infinite Products.