This book presents a unified view of calculus in which theory and practice reinforces each other. It is about the theory and applications of derivatives (mostly partial), integrals, (mostly multiple or improper), and infinite series (mostly of functions rather than of numbers), at a deeper level than is found in the standard calculus books. Chapter topics cover: Setting the Stage, Differential Calculus, The Implicit Function Theorem and Its Applications, Integral Calculus, Line and Surface Integrals—Vector Analysis, Infinite Series, Functions Defined by Series and Integrals, and Fourier Series. For individuals with a sound knowledge of the mechanics of one-variable calculus and an acquaintance with linear algebra.
This book treats partial derivatives, multiple integrals, and infinite series of functions at a deeper level than is found in most standard calculus texts, emphasizing intuitive understanding rather than formal proofs and technical definitions. Technical definitions are presented with informal arguments and ideas, sometimes involving infinitesimals, that provide more insight than a more rigorous approach. Worked examples and exercises range from routine calculations to theoretical arguments. A sound knowledge of the mechanics of one-variable calculus is required, and some experience with infinite series and partial derivatives is helpful. The author teaches mathematics at the University of Washington. Annotation c. Book News, Inc., Portland, OR (booknews.com)