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Zusatztext "Falconer's book is excellent in many respects and the reviewer strongly recommends it. May every university library own a copy! or three! And if you're a student reading this! go check it out today!." (Mathematical Association of America! 11 June 2014) Informationen zum Autor Kenneth Falconer , University of St Andrews, UK. Klappentext 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 www.wileyeurope.com/fractal Leads onto the more advanced sequel Techniques in Fractal Geometry (also by Kenneth Falconer and available from Wiley) Zusammenfassung This comprehensive and popular textbook makes fractal geometry accessible to final-year undergraduate math or physics majors, while also serving as a reference for research mathematicians or scientists. This up-to-date edition covers introductory multifractal theory, random fractals, and modern applications in finance and science. Inhaltsverzeichnis Preface to the first edition ix Preface to the second edition xiii Preface to the third edition xv Course suggestions xvii Introduction xix Part I Foundations 1 1 Mathematical background 3 1.1 Basic set theory 3 1.2 Functions and limits 7 1.3 Measures and mass distributions 11 1.4 Notes on probability theory 17 1.5 Notes and references 24 Exercises 24 2 Box-counting dimension 27 2.1 Box-counting dimensions 27 2.2 Properties and problems of box-counting dimension 34 2.3 Modified box-counting dimensions 38 2.4 Some other definitions of dimension 40 2.5 Notes and references 41 Exercises 42 3 Hausdorff and packing measures and dimensions 44 3.1 Hausdorff measure 44 3.2 Hausdorff dimension 47 3.3 Calculation of Hausdorff dimension - simple examples 51 3.4 Equivalent definitions of Hausdorff dimension 53 3.5 Packing measure and dimensions 54 3.6 Finer definitions of dimension 57 3.7 Dimension prints 58 3.8 Porosity 60 3.9 Notes and references 63 Exercises 64 4 Techniques for calculating dimensions 66 4.1 Basic methods 66 4.2 Subsets of finite measure 75 4.3 Potential theoretic methods 77 4.4 ...
