Ebook: Calculus and Analysis in Euclidean Space

This book came into being as lecture notes for a course at Reed College on multivariable calculus and analysis. The setting is n-dimensional Euclidean space, with the material on differentiation culminating in the inverse function theorem and its consequences, and the material on integration culminating in the general fundamental theorem of integral calculus (often called Stokes’s theorem) and some of its consequences in turn. The prerequisite is a proof- based course in one-variable calculus and analysis. Some familiarity with the complex number system and complex mappings is occasionally assumed as well, but the reader can get by without it.