Calculus: A Complete Course, 10th edition

Proven in North America and abroad, this classic text has earned a reputation for excellent accuracy and mathematical rigour. 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.