Functions of Several Variables

16This new edition of FUNCTIONS OF SEVERAL VARIABLES is an extensive revision. Like the first edition it presents a thorough introduction to differential and integral calculus, including the integration of differential forms on manifolds. A new chapter on elementary topology makes the book more complete as an advanced calculus text; sections have been added introducing physical applications in thermodynamics, fluid dynamics, and classical rigid body mechanics.041: 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.