Basic Analysis

A study of basic analysis and related topics. It presents important theorems in measure and integration, an introduction to functional analysis, the big advanced calculus theorems about the Frechet derivative including the implicit function theorem, and other topics including fixed point theorems and applications, the Brouwer degree, and an introduction to the generalized Riemann integral. Although there are some abstract topics, the emphasis is on analysis which takes place in the context of n dimensional Euclidean space. The volume is directed to advanced undergraduates and beginning graduate students in maths and physical science who are interested in analysis, and is self-contained for this audience. It could be used as a textbook for a two-semester course.