The Calculus Lifesaver. All the Tools You Need To Excel at Calculus
On more than 700 pages the author explains standard calculus material for real functions of one real variable (from limits of functions to ordinary differential equations). The explanation is based not only on some theorems but mainly on carefully selected examples and their elaboration. It takes more time and more pages but it is surely convenient for students to understand methods used in this part of calculus both from theoretical and practical points of view. Care is devoted to the introductory chapters dealing with basic properties of functions, as can be seen from the distribution of pages in the book. The first 300 pages are devoted to functions, their limits and derivatives, graphs of functions, optimization and linearization. Almost 200 pages deal with integration and its applications (volumes, lengths and surfaces), while the rest is devoted to sequences and series (about 100 pages, including Taylor series) and differential equations (about 25 pages). Proofs of some theorems are contained in the last 40 pages of the book. Videotapes of the whole course are available for free on the Internet.