Overview

Written for mathematicians, engineers, researchers in experimental science, and anyone interested in fractals, this book presents the fundamentals of curve analysis with a new and clear introduction to fractal dimension. It explains the geometrical and analytical properties of trajectories, aggregate contours, geographical coastlines, profiles of rough surfaces, and other curves of finite and fractal length. The approach is through precise definitions from which properties are deduced and applications and computational methods are derived. Written without the traditional heavy symbolism of mathematics texts, this book requires two years of calculus as a prerequisite to understanding. This text also contains material appropriate for graduate coursework in curve analysis and/or fractal dimension.

Full Product Details

Author:   Claude Tricot ,  M. Mendes France
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Edition:   1995 ed.
Dimensions:   Width: 15.60cm , Height: 2.00cm , Length: 23.40cm
Weight:   1.440kg
ISBN:  

9780387940953

ISBN 10:   0387940952
Pages:   324
Publication Date:   18 November 1994
Audience:   College/higher education ,  Professional and scholarly ,  Undergraduate ,  Postgraduate, Research & Scholarly
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

I. Sets of Null Measure on the Line.- 1. Perfect Sets and Their Measure.- 2. Covers and Dimension.- 3. Contiguous Intervals and Dimension.- II. Rectifiable Curves.- 4. What Is a Curve?.- 5. Polygonal Curves and Length.- 6. Parameterized Curves, Support of a Measure.- 7. Local Geometry of Rectifiable Curves.- 8. Length, by Intersections with Straight Lines.- 9. The Length by the Area of Centered Balls.- III. Nonrectifiable Curves.- 10. Curves of Infinite Length.- 11. Fractal Curves.- 12. Graphs of Nondifferentiable Functions.- 13. Curves Constructed by Similarities.- 14. Deviation, and Expansive Curves.- 15. The Constant-Deviation Variable-Step Algorithm.- 16. Scanning a Curve with Straight Lines.- 17. Lateral Dimension of a Curve.- 18. Dimensional Homogeneity.- IV. Annexes, References and Index.- A. Upper Limit and Lower Limit.- A.1 Convergence.- A.2 Nonconvergent sequences.- A.3 Nonconvergent functions.- A.5 Some applications.- B. Two Covering Lemmas.- B.1 Vitali’s lemma.- B.2 Covers by homothetic convex sets.- C. Convex Sets in the Plane.- C.1 Convexity.- C.2 Size of a convex set.- C.3 Breadth of a convex set.- C.4 Area of a convex set.- C.5 Convex hull.- C.6 Perimeter of the convex hull.- C.7 Area of the convex hull of a curve.- References.

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