This second of two Exercises in Analysis volumes covers problems in five
core topics of mathematical analysis: Function Spaces, Nonlinear and
Multivalued Maps, Smooth and Nonsmooth Calculus, Degree Theory and Fixed
Point Theory, and Variational and Topological Methods. Each of five
topics corresponds to a different chapter with inclusion of the basic
theory and accompanying main definitions and results, followed by
suitable comments and remarks for better understanding of the material.
Exercises/problems are presented for each topic, with solutions
available at the end of each chapter. The entire collection of exercises
offers a balanced and useful picture for the application surrounding
each topic.
This nearly encyclopedic coverage of exercises in mathematical analysis
is the first of its kind and is accessible to a wide readership.
Graduate students will find the collection of problems valuable in
preparation for their preliminary or qualifying exams as well as for
testing their deeper understanding of the material. Exercises are
denoted by degree of difficulty. Instructors teaching courses that
include one or all of the above-mentioned topics will find the exercises
of great help in course preparation. Researchers in analysis may find
this Work useful as a summary of analytic theories published in one
accessible volume.