This book evolved over a period of years as the authors taught classes in variational calculus and applied functional analysis to graduate students in engineering and mathematics. The book has likewise been influenced by the authors’ research programs that have relied on the application of functional analytic principles to problems in variational calculus, mechanics and control theory. One of the most difficult tasks in preparing to utilize functional, convex, and set-valued analysis in practical problems in engineering and physics is the intimidating number of definitions, lemmas, theorems and propositions that constitute the foundations of functional analysis. It cannot be overemphasized that functional analysis can be a powerful tool for analyzing practical problems in mechanics and physics. However, many academicians and researchers spend their lifetime studying abstract mathematics. It is a demanding field that requires discipline and devotion. It is a trite analogy that mathematics can be viewed as a pyramid of knowledge, that builds layer upon layer as more mathematical structure is put in place. The difficulty lies in the fact that an engineer or scientist typically would like to start somewhere “above the base” of the pyramid. Engineers and scientists are not as concerned, generally speaking, with the subtleties of deriving theorems axiomatically. Rather, they are interested in gaining a working knowledge of the applicability of the theory to their field of interest.Monday, September 19, 2011
Convex Functional Analysis by Andrew J. Kurdila and Michael Zabarankin
This book evolved over a period of years as the authors taught classes in variational calculus and applied functional analysis to graduate students in engineering and mathematics. The book has likewise been influenced by the authors’ research programs that have relied on the application of functional analytic principles to problems in variational calculus, mechanics and control theory. One of the most difficult tasks in preparing to utilize functional, convex, and set-valued analysis in practical problems in engineering and physics is the intimidating number of definitions, lemmas, theorems and propositions that constitute the foundations of functional analysis. It cannot be overemphasized that functional analysis can be a powerful tool for analyzing practical problems in mechanics and physics. However, many academicians and researchers spend their lifetime studying abstract mathematics. It is a demanding field that requires discipline and devotion. It is a trite analogy that mathematics can be viewed as a pyramid of knowledge, that builds layer upon layer as more mathematical structure is put in place. The difficulty lies in the fact that an engineer or scientist typically would like to start somewhere “above the base” of the pyramid. Engineers and scientists are not as concerned, generally speaking, with the subtleties of deriving theorems axiomatically. Rather, they are interested in gaining a working knowledge of the applicability of the theory to their field of interest.
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