An outstanding textbook, complete with examples, exercises, and solutions, for an advanced calculus course in which differential forms can be used to introduce the subject. Enriching reading for its modern viewpoint and techniques. The diverse set of topics from which advanced calculus courses are created are presented here in beautiful unifying generalization. This text has been adopted at: University of California, Davis Layfayette College, Easton, PA Western Illinois University, Macomb University of Michigan, Ann Arbor Eastern Washington University, Cheney