Offering a presentation of calculus with applications to engineering and the sciences, this book emphasizes the methods and applications of the calculus with some coverage of relevant theory, including functions, limits, continuity, differentiation, integrations in higher dimensions, and line and surface integrals. Particular attention is paid to those aspects of calculus that are important in developing effective problem-solving methods - often involving estimating errors or constructing numerical approximations. The material features many applications. The book provides treatment of topics such as comparison tests for improper integrals, use of power series representations for functions, and the relation between linear approximations and differentiation. Other topics covered include elementary transcendental functions, infinite series, Taylor's approximation, polar coordinates, and vectors and three-dimensional geometry.