This is a revision of the 1977 edition, which has been reviewed [MR0463372]. The changes include addition of new problems, rewriting and clarifying parts of the text and the inclusion of the answers to the odd-numbered problems. The information in the text provides a solid theoretical foundation for students who have completed the standard calculus course and now wish to move on to a more complete treatment of the material. The sixteen chapter titles are listed in the review cited above. Here is a very brief sample of the material. Integration is treated first using the Darboux definition and showing its equivalence to the Riemann definition (in Chapter 5 for one variable and in Chapter 8 for n variables). Functions of bounded variation and the Riemann-Stieltjes integral are treated in Chapter 12. Line integrals, Green's theorem and Stokes' theorem are treated in Chapter 16. An introduction to metric spaces is given in Chapters 6 and 12 and the theory is used effectively at various points throughout the remainder of the text. For example, the idea of a contraction mapping is used to show the convergence of Newton's method in certain cases. The numerous worked examples help to clarify many concepts. Students should find the text very readable and not be overwhelmed with excessive notation.
Reviewer: Janusz, Gerald J. [form MathSciNet]