This introduction to mathematical analysis contains graphs to help with the visualization of important ideas, and includes historial and philosophical discussions. Topics covered include Euclidean squares and functions of bounded variation.

1. The Structure of the Real Numbers: Sequences
2. Euclidean Spaces
3. Continuity
4. Differentiation
5. Functions of Bounded Variations
6. The Riemann Integral
7. The Riemann-Stieltjes Integral
8. Differential Calculus in R^n
9. Vector-Valued Functions
10. Multiple Integrals
11. Infinite Series
12. Series of Functions
13. Improper Integrals
14. Fourier Series

A. Axioms for the Real Numbers R
B. Set Theory
C. Functions
D. Polynomials
References and Additional Readings
Index

Steven A. Douglass

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