Mathematical Analysis: Foundations and Advanced Techniques for Functions of Several Variables - Softcover
Synopsis
"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. It concludes 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 recently published by the authors, is the motivation for understanding the subject through examples, observations, exercises, and illustrations.
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Review
From the reviews:
"This book is suitable as a text for graduate students. Photographs of Banach, Fréchet, Hausdorff, Hilbert and some others mathematicians are imprinted in order to involve [the reader] in the work of mathematicians."—Zentralblatt MATH
"This volume is an English translation and revised edition of a former Italian version published in 2000. … This nice book is recommended to advanced undergraduate and graduate students. It can serve also as a valuable reference for researchers in mathematics, physics, and engineering." (L. Kérchy, Acta Scientiarum Mathematicarum, Vol. 74, 2008)
“The book ‘M. Giaquinta, G. Modica: Mathematical Analysis. Linear and Metric Structures and Continuity’ is a lovely book which should be in the bookcase of every expert in mathematical analysis.” (Dagmar Medková, Mathematica Bohemica, Issue 2, 2010)
“This book offers a self-contained introduction to certain central topics of functional analysis and topology for advanced undergraduate and graduate students. … the clear and self-contained style recommend the book for self-study, offering a quick introduction to a number of central notions of functional analysis and topology. A large number of exercises and historical remarks add to the pleasant overall impression the book leaves.” (M. Kunzinger, Monatshefte für Mathematik, Vol. 157 (2), June, 2009)
From the Back Cover
This self-contained work on linear and metric structures focuses on studying continuity and its applications to finite- and infinite-dimensional spaces.
The book is divided into three parts. The first part introduces the basic ideas of linear and metric spaces, including the Jordan canonical form of matrices and the spectral theorem for self-adjoint and normal operators. The second part examines the role of general topology in the context of metric spaces and includes the notions of homotopy and degree. The third and final part is a discussion on Banach spaces of continuous functions, Hilbert spaces and the spectral theory of compact operators.
Mathematical Analysis: Linear and Metric Structures and Continuity motivates the study of linear and metric structures with examples, observations, exercises, and illustrations. It may be used in the classroom setting or for self-study by advanced undergraduate and graduate students and as a valuable reference for researchers in mathematics, physics, and engineering.
Other books recently published by the authors include: Mathematical Analysis: Functions of One Variable, and Mathematical Analysis: Approximation and Discrete Processes. This book builds upon the discussion in these books to provide the reader with a strong foundation in modern-day analysis.
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