Differential Calculus of One Variable

Abstract

Students taking the course on mathematical methods generally protested vigorously when told that we were going to start with a review of calculus, on the grounds that they knew it all. Now, that proved to be the case for some, while for many it was somewhat different: either they once knew it, or thought they once knew it, or actually knew someone who did, and so on. Since everything hinges on calculus rather heavily, we will play it safe and review it in the first three chapters. However, to keep the interest level up, the review will be brief and only subtleties related to differential and integral calculus will be discussed at any length. The main purpose of the review is to go through results you probably know and ask where they come from and how they are interrelated and also to let you know where you really stand. If you find any portion where you seem to be weak, you must find a book on calculus, work out many more problems than are assigned here, and remedy the defect at once.