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falconer k fractal geometry mathematical foundations applications 3ed 2014

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Textbook in PDF and DJVU formats The seminal text on fractal geometry for students and researchers: extensively revised and updated with new material, notes and references that reflect recent directions. Interest in fractal geometry continues to grow rapidly, both as a subject that is fascinating in its own right and as a concept that is central to many areas of mathematics, science and scientific research. Since its initial publication in 1990 Fractal Geometry: Mathematical Foundations and Applications has become a seminal text on the mathematics of fractals. The book introduces and develops the general theory and applications of fractals in a way that is accessible to students and researchers from a wide range of disciplines. Fractal Geometry: Mathematical Foundations and Applications is an excellent course book for undergraduate and graduate students studying fractal geometry, with suggestions for material appropriate for a first course indicated. The book also provides an invaluable foundation and reference for researchers who encounter fractals not only in mathematics but also in other areas across physics, engineering and the applied sciences. Provides a comprehensive and accessible introduction to the mathematical theory and applications of fractals Carefully explains each topic using illustrative examples and diagrams Includes the necessary mathematical background material, along with notes and references to enable the reader to pursue individual topics Features a wide range of exercises, enabling readers to consolidate their understanding Supported by a website with solutions to exercises and additional material http://www.wileyeurope.com/fractal Leads onto the more advanced sequel Techniques in Fractal Geometry. Foundations. Mathematical background. Box-counting dimension. Hausdorff and packing measures and dimensions. Techniques for calculating dimensions. Local structure of fractals. Projections of fractals. Products of fractals. Intersections of fractals. Applications and examples. Iterated function systems – self-similar and self-affine sets. Examples from number theory. Graphs of functions. Examples from pure mathematics. Dynamical systems. Iteration of complex functions – Julia sets and the Mandelbrot set. Brownian motion and Brownian surfaces. Multifractal measures. Physical applications

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falconer k fractal geometry mathematical foundations applications 3ed 2014

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