The text is for a two semester course in advanced calculus. It develops the basic ideas of calculus rigorously but with an eye to showing how mathematics connects with other areas of science and engineering. In particular, effective numerical computation is developed as an important aspect of mathematical analysis. * Maintains a rigorous presentation of the main ideas of advanced calculus, interspersed with applications that show how to analyze real problems * Includes a wide range of examples and exercises drawn from mechanics, biology, chemical engineering and economics * Describes links to numerical analysis and provides opportunities for computation; some MATLAB codes are available on the author"s webpage * Enhanced by an informal and lively writing style