Postmodern Analysis

This is an introduction to advanced analysis that supports a modern presentation with concrete examples and applications, in particular in the areas of calculus of variations and partial differential equations. The book aims to impart a working knowledge of the key methods of contemporary analysis, in particular those that are also relevant for application in physics. It provides a streamlined introduction to the fundamental concepts of Banach space and Lebesgue integration theory and the basic notions of the calculus of variations, including Sobolev space theory. The expanded third edition contains all-new material on cover theorems, and added material on properties of various classes of weakly differential functions.