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Fractal-Based Methods in Analysis (Paperback, 2012 ed.)
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Fractal-Based Methods in Analysis (Paperback, 2012 ed.)
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Discovery Miles: 30 650
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The idea of modeling the behaviour of phenomena at multiple scales
has become a useful tool in both pure and applied mathematics.
Fractal-based techniques lie at the heart of this area, as fractals
are inherently multiscale objects; they very often describe
nonlinear phenomena better than traditional mathematical models. In
many cases they have been used for solving inverse problems arising
in models described by systems of differential equations and
dynamical systems. "Fractal-Based Methods in Analysis" draws
together, for the first time in book form, methods and results from
almost twenty years of research in this topic, including new
viewpoints and results in many of the chapters. For each topic the
theoretical framework is carefully explained using examples and
applications. The second chapter on basic iterated function systems
theory is designed to be used as the basis for a course and
includes many exercises. This chapter, along with the three
background appendices on topological and metric spaces, measure
theory, and basic results from set-valued analysis, make the book
suitable for self-study or as a source book for a graduate course.
The other chapters illustrate many extensions and applications of
fractal-based methods to different areas. This book is intended for
graduate students and researchers in applied mathematics,
engineering and social sciences. Herb Kunze is a professor of
mathematics at the University of Guelph in Ontario. Davide La Torre
is an associate professor of mathematics in the Department of
Economics, Management and Quantitative Methods of the University of
Milan. Franklin Mendivil is a professor of mathematics at Acadia
University in Nova Scotia. Edward Vrscay is a professor in the
department of Applied Mathematics at the University of Waterloo in
Ontario. The major focus of their research is on fractals and the
applications of fractals.
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