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This new edition, like the first, presents a thorough introduction to differential and integral calculus, including the integration of differential forms on manifolds. However, an additional chapter on elementary topology makes the book more complete as an advanced calculus text, and sections have been added introducing physical applications in thermodynamics, fluid dynamics, and classical rigid body mechanics.
1: Euclidean spaces. 2: Elementary topology of E. 3: Differentiation of real-valued functions. 4: Vector-valued functions of several variables. 5: Integration. 6: Curves and line integrals. 7: Exterior algebra and differential calculus. 8: Integration on manifolds. Appendix 1: Axioms for a vector space. Appendix 2: Mean value theorem. Appendix 3: Review of Riemann integration. Appendix 4: Monotone functions. References. Answers to problems. Index.