New publisher! Corrected version! Demonstrating analytical and numerical techniques for attacking problems in the application of mathematics, this well-organized, clearly written text presents the logical relationship and fundamental notations of analysis. Buck discusses analysis not solely as a tool, but as a subject in its own right. This skill-building volume familiarizes students with the language, concepts, and standard theorems of analysis, preparing them to read the mathematical literature on their own. The text revisits certain portions of elementary calculus and gives a systematic, modern approach to the differential and integral calculus of functions and transformations in several variables, including an introduction to the theory of differential forms. The material is structured to benefit those students whose interests lean toward either research in mathematics or its applications.