Advanced Calculus

Patrick M. Fitzpatrick, University of Maryland, College Park, MD, USA

• PrefacePreliminaries1. Tools for Analysis2. Convergent Sequences3. Continuous Functions4. Differentiation5. Elementary Functions as Solutions of Differential Equations6. Integration: Two Fundamental Theorems7. Integration: Further Topics8. Approximation by Taylor Polynomials9. Sequences and Series of Functions10. The Euclidean Space Rn11. Continuity, Compactness, and Connectedness12. Metric Spaces13. Differentiating Functions of Several Variables14. Local Approximation of Real-Valued Functions15. Approximating Nonlinear Mapping by Linear Mappings16. Images and Inverses: The Inverse Function Theorem17. The Implicit Function Theorem and its Applications18. Integrating Functions of Several Variables19. Iterated Integration and Changes of Variables20. Line and Surface IntegralsAppendix A: Consequences of the Field and Positivity AxiomsAppendix B: Linear AlgebraIndex

This is a well-written and well-structured book with clearly explained proofs and a good supply of exercises, some of them are quite challenging. It is this reviewer's opinion that the volume should be an excellent and useful tool for undergraduate students." - Teodora-Liliana Radulescu, Zentralblatt MATH