Fractal Geometry - Mathematical Foundations and Applications

Klappentext Since its original publication in 1990! Kenneth Falconer's Fractal Geometry: Mathematical Foundations and Applications has become a seminal text on the mathematics of fractals. It introduces the general mathematical theory and applications of fractals in a way that is accessible to students from a wide range of disciplines. This new edition has been extensively revised and updated. It features much new material! many additional exercises! notes and references! and an extended bibliography that reflects the development of the subject since the first edition.* Provides a comprehensive and accessible introduction to the mathematical theory and applications of fractals.* Each topic is carefully explained and illustrated by examples and figures.* Includes all necessary mathematical background material.* Includes notes and references to enable the reader to pursue individual topics.* Features a wide selection of exercises! enabling the reader to develop their understanding of the theory.* Supported by a Web site featuring solutions to exercises! and additional material for students and lecturers.Fractal Geometry: Mathematical Foundations and Applications is aimed at undergraduate and graduate students studying courses in fractal geometry. The book also provides an excellent source of reference for researchers who encounter fractals in mathematics! physics! engineering! and the applied sciences.Also by Kenneth Falconer and available from Wiley:Techniques in Fractal GeometryISBN 0-471-95724-0Please click here to download solutions to exercises found within this title:http://www.wileyeurope.com/fractal Inhaltsverzeichnis Preface.Preface to the second edition.Course suggestions.Introduction.Notes and references.PART I: FOUNDATIONS.Chapter 1: Mathematical background.1.1 Basic set theory.1.2 Functions and limits.1.3 Measures and mass distributions.1.4 Notes on probability theory.1.5 Notes and references.Exercises.Chapter 2: Hausdorff measure and dimension.2.1 Hausdorff measure.2.2 Hausdorff dimension.2.3 Calculation of Hausdorff dimension-simple examples.*2.4 Equivalent definitions of Hausdorff dimension.*2.5 Finer definitions of dimension.2.6 Notes and references.Exercises.Chapter 3: Alternative definitions of dimension.3.1 Box-counting dimensions.3.2 Properties and problems of box-counting dimension.*3.3 Modified box-counting dimensions.*3.4 Packing measures and dimensions.3.5 Some other definitions of dimension.3.6 Notes and references.Exercises.Chapter 4: Techniques for calculating dimensions.4.1 Basic methods.4.2 Subsets of finite measure.4.3 Potential theoretic methods.*4.4 Fourier transform methods.4.5 Notes and references.Exercises.Chapter 5: Local structure of fractals.5.1 Densities.5.2 Structure of 1-sets.5.3 Tangents to s-sets.5.4 Notes and references.Exercises.Chapter 6: Projections of fractals.6.1 Projections of arbitrary sets.6.2 Projections of s-sets of integral dimension.6.3 Projections of arbitrary sets of integral dimension.6.4 Notes and references.Exercises.Chapter 7: Products of fractals.7.1 Product formulae.7.2 Notes and references.Exercises.Chapter 8: Intersections of fractals.8.1 Intersection formulae for fractals.*8.2 Sets with large intersection.8.3 Notes and references.Exercises.PART II: APPLICATIONS AND EXAMPLES.Chapter 9: Iterated function systems-self-similar and self-affine sets.9.1 Iterated function system.9.2 Dimensions of self-similar sets.9.3 Some variations.9.4 Self-affine sets.9.5 Applications to encoding images.9.6 Notes and references.Exercises.Chapter 10: Examples from number theory.10.1 Distribution of digits of numbers.10.2 Continued fractions.10.3 Diophantine approximation.10.4 Notes and references.Exercises.Chapter 11: Graphs of functions.11.1 Dimensions of graphs.*11.2 Autocorrelation of fractal functions.11.3 Notes and references.Exercises.Chapter 12...

Dettagli sul prodotto

• Autori: Falconer, K. J. Falconer, K.j. Falconer, Kenneth Falconer
• Editore: Wiley, John and Sons Ltd
• Lingue: Inglese
• Formato: Tascabile
• Pubblicazione: 19.09.2003
• EAN: 9780470848623
• ISBN: 978-0-470-84862-3
• Pagine: 366
• Categoria: Scienze naturali, medicina, informatica, tecnica > Matematica > Geometria