Research Catalog

Title

Mathematical TeX by example / Arvind Borde.

Author

Borde, Arvind, 1955-

Publication

Boston : Academic Press, ©1993.

Items in the Library & Off-site

Details

Description

xi, 352 pages : illustrations; 24 cm

Summary

• "These are exciting times for mathematics, science, and technology. One of the fields that has been receiving great attention is Chaos Theory. Actually, this is not a single discipline, but a potpourri of nonlinear dynamics, nonequilibrium thermodynamics, information theory, and fractal geometry. In the less than two decades that Chaos Theory has become a major part of mathematics and physics, it has become evident that the old paradigm of determinism is insufficient if we are to understand - and perhaps solve - real life problems. Curiously, many of these problems are deterministic, but they are intertwined with randomness and chance. Thus the deterministic laws of physics coexist with the laws of probability. Consequently, uncertainty arises and unpredictability occurs, characteristic of complex systems.".
• "In its short lifetime Chaos Theory has already helped us gain insights into problems that in the past we found intractable. Examples of such problems include weather, turbulence, cardiological and neurophysiological episodes, economic restructuring, financial transactions, policy analysis, and decision making. Admittedly, we can as yet solve only relatively simple problems, but much progress has been made and we are now able to observe complex problems from new vantage points that provide us with numerous benefits. One such benefit is the universality of Chaos Theory in its applicability to different situations, which enables us to look at communal problems in an interdisciplinary manner, so that persons of different backgrounds can communicate with one another. Chaos Theory also enables us to reason in a holistic manner, rather than being constrained by simplistic reductionism. Finally, it is gratifying that the mathematics is not intimidating, and one can accomplish much with a personal computer or even a handheld calculator."--BOOK JACKET.

Subject

• TeX (Computer file)
• Computerized typesetting
• Mathematics printing > Computer programs
• computerized composition (pre-print process)
• TeX
• Software basico

Note

• "Also covers AmS-TeX"--Cover.

Bibliography (note)

• Includes bibliographical references (p. 233-239) and index.

Contents

• 1. Living with Complexity -- Characteristics of Complexity -- Laplace's Demon -- Nonlinearity -- A Sneak Preview of Chaos Theory -- Degrees of Freedom and Numbers -- Dynamical Systems -- Scope -- Quo Vadis? Reduction and Holism -- 2. Meta-Quanitification of Complexity -- Facing the New Realities -- Hierarchical Approach -- Geometric Approach -- Algorithmic Complexity -- 3. The Anatomy of Systems and Structures -- Open, Closed, and Isolated Systems -- Phase Space -- Equilibrium and Nonequilibrium -- Stability and Instability -- Parameters to Evaluate Equilibrium -- Rayleigh-Benard Instability -- Irreversibility -- 4. Attractors -- Fixed-Point Attractors -- Limit Cycles -- Torus Attractors -- Strange Attractors -- Bernoulli Shift -- Lyapunov Exponential Coefficient -- Belousov-Zhabotinsky Reaction -- 5. Rapid Growth -- Malthus's Theory and the Exponential Equation -- Fibonacci Series -- 6. The Logistic Curve -- Verhulst's Equation -- Clues for Technological R&D Planning -- Lotka-Volterra Equations -- 7. The Discrete Logistic Equation -- The Discrete Logistic Curve -- The Morphology of the Discrete Logistic Equation -- Return Maps -- Bifurcation Diagram -- Feigenbaum Universal Numbers -- Multivariable Equations -- 8. The Different Personalities of Entropy -- Is Entropy for Real? -- Why Muddy the Waters with Entropy? -- Macroscopic Entropy -- Statistical Entropy -- Dynamic Entropies -- 9. Dimensions and Scaling -- Dimensions
• Hausdorff-Besicovitch Dimension -- Embedding Dimension -- Scaling -- 10. Gallery of Monsters -- Background -- Julia and Mandelbrot Sets -- Barnsley's Chaos Game -- 11. The Diagnostics and Control of Chaos -- Time Series -- Time Series Analysis -- Log-Normal Distribution and 1/f Noise -- Ising Model -- Chaos Diagnostics -- Chaos Control -- Start Your Own Chaos Laboratory -- 12. Discussion Topics.

ISBN

• 0121176452
• 9780121176457
• 0121559408
• 9780121559403

LCCN

92029048

OCLC

• ocm26398817
• 26398817
• SCSB-9340424

Owning Institutions

Princeton University Library