Designed for a one-semester advanced calculus course, Advanced Calculus explores the theory of calculus and highlights the connections between calculus and real analysis -- providing a mathematically sophisticated introduction to functional analytical concepts. The text is interesting to read and includes many illustrative worked-out examples and instructive exercises, and precise historical notes to aid in further exploration of calculus.
Part I. Fundamentals1. Sets, Numbers, and Functions2. Sequences3. Infinite Series4. Continuity5. Differentiation6. IntegrationPart II. Advanced Topics7. Commutation of Limit Operations