An accessible but rigorous development of basic analysis
that features extended discussions of important ideas, detailed examples
of difficult proofs, and reinforcement of basic ideas through repeated
exposure in different contexts.
emphasizes WHY various mathematical facts are true.
avoids as mush as possible the distraction of purely rote,
computational aspects of calculus, and reduces all exercises (mainly
composed of proofs) to a smaller series of steps.
presents each theoretical idea with several paralleling
examples proceeding it.
1. The Real Number System.
2. Functions, Limits, Continuity.
3. Differentiation and Integration.
4. Sequences and Series.
5. Calculus in Two Dimensions.
6. Line Integrals and Green's Theorem.
7. Complex Analysis.