"Mathematical Analysis: Foundations and Advanced Techniques for
Functions of Several Variables" builds upon the basic ideas and
techniques of differential and integral calculus for functions of
several variables, as outlined in an earlier introductory volume.
The presentation is largely focused on the foundations of measure
and integration theory.
The book begins with a discussion of the geometry of Hilbert
spaces, convex functions and domains, and differential forms,
particularly k-forms. The exposition continues with an introduction
to the calculus of variations with applications to geometric optics
and mechanics.The authorsconclude with the study of measure and
integration theory - Borel, Radon, and Hausdorff measures and the
derivation of measures. An appendix highlights important
mathematicians and other scientists whose contributions have made a
great impact on the development of theories in analysis.
This work may be used as a supplementary text in the classroom
or for self-study by advanced undergraduate and graduate students
and as a valuable reference for researchers in mathematics,
physics, and engineering. One of the key strengths of this
presentation, along with the other four books on analysis published
by the authors, is the motivation for understanding the subject
through examples, observations, exercises, and illustrations."
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