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Unlike some other reproductions of classic texts (1) We have not
used OCR(Optical Character Recognition), as this leads to bad
quality books with introduced typos. (2) In books where there are
images such as portraits, maps, sketches etc We have endeavoured to
keep the quality of these images, so they represent accurately the
original artefact. Although occasionally there may be certain
imperfections with these old texts, we feel they deserve to be made
available for future generations to enjoy.
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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