This classic text has earned a reputation for excellent accuracy and mathematical rigour. The 10th edition continues in the pattern of the 8th and 9th editions, adding important, but overlooked, topics while clarifying old ones, and building on the solid core emplaced in prior editions. It remains the only mainstream textbook that covers sufficient conditions for maxima and minima in higher dimensions. In the classical curriculum, differentials are defined as linear combinations of other differentials. But then later they are also asserted to be products of differentials, without explanation. This edition clarifies, connecting these new objects as they arise. Metrics are a rather fuzzy topic in most texts, leaving the questions that arc length implies hanging. The exploration of these questions leads to new gateway topics, including spherical geometry (as in navigation), and special relativity, which both emerge rather effortlessly once the metric concept is properly in place.

The 10th edition is suitable for a semester course in differential equations, in addition to the existing standard material suitable for four semesters of calculus. Not only can it be used to deliver five standard courses of conventional material, it can do much more through some of the unique topics and approaches, which can be added or overlooked by the instructor without penalty. There is no other calculus book that deals better with computers and mathematics through Maple and now Python, while treating unique but important applications from information theory to Levy distributions.