عنوان
پدید آورنده
موضوع
رده
QA614.8 .S34 2012eb
QA614
.
8
.
S34
2012eb
کتابخانه
محل استقرار
INTERNATIONAL STANDARD BOOK NUMBER
(Number (ISBN
0486275329
(Number (ISBN
9780486275321
Erroneous ISBN
0486485943
Erroneous ISBN
9780486485942
TITLE AND STATEMENT OF RESPONSIBILITY
Title Proper
Invitation to dynamical systems /
General Material Designation
[Book]
First Statement of Responsibility
Edward R. Scheinerman.
EDITION STATEMENT
Edition Statement
Dover ed.
.PUBLICATION, DISTRIBUTION, ETC
Place of Publication, Distribution, etc.
Mineola, N.Y. :
Name of Publisher, Distributor, etc.
Dover Publications,
Date of Publication, Distribution, etc.
2012.
PHYSICAL DESCRIPTION
Specific Material Designation and Extent of Item
1 online resource (xvii, 373 pages) :
Other Physical Details
illustrations
SERIES
Series Title
Dover Books on Mathematics
GENERAL NOTES
Text of Note
Originally published: Upper Saddle River, N.J. : Prentice-Hall, 1996.
INTERNAL BIBLIOGRAPHIES/INDEXES NOTE
Text of Note
Includes bibliographical references (pages 369-370) and index.
CONTENTS NOTE
Text of Note
Cover Page; Title Page; Copyright Page; Dedication; Contents; Preface; 1 Introduction; 1.1 What is a dynamical system?; 1.1.1 State vectors; 1.1.2 The next instant: discrete time; 1.1.3 The next instant: continuous time; 1.1.4 Summary; Problems; 1.2 Examples; 1.2.1 Mass and spring; 1.2.2 RLC circuits; 1.2.3 Pendulum; 1.2.4 Your bank account; 1.2.5 Economic growth; 1.2.6 Pushing buttons on your calculator; 1.2.7 Microbes; 1.2.8 Predator and prey; 1.2.9 Newton's Method; 1.2.10 Euler's method; 1.2.11 "Random" number generation; Problems; 1.3 What we want; what we can get; 2 Linear Systems.
Text of Note
2.1 One dimension2.1.1 Discrete time; 2.1.2 Continuous time; 2.1.3 Summary; Problems; 2.2 Two (and more) dimensions; 2.2.1 Discrete time; 2.2.2 Continuous time; 2.2.3 The nondiagonalizable case*; Problems; 2.3 Examplification: Markov chains; 2.3.1 Introduction; 2.3.2 Markov chains as linear systems; 2.3.3 The long term; Problems; 3 Nonlinear Systems 1: Fixed Points; 3.1 Fixed points; 3.1.1 What is a fixed point?; 3.1.2 Finding fixed points; 3.1.3 Stability; Problems; 3.2 Linearization; 3.2.1 One dimension; 3.2.2 Two and more dimensions; Problems; 3.3 Lyapunov functions.
Text of Note
3.3.1 Linearization can fail3.3.2 Energy; 3.3.3 Lyapunov's method; 3.3.4 Gradient systems; Problems; 3.4 Examplification: Iterative methods for solving equations; Problems; 4 Nonlinear Systems 2: Periodicity and Chaos; 4.1 Continuous time; 4.1.1 One dimension: no periodicity; 4.1.2 Two dimensions: the Poincaré-Bendixson theorem; 4.1.3 The Hopf bifurcation*; 4.1.4 Higher dimensions: the Lorenz system and chaos; Problems; 4.2 Discrete time; 4.2.1 Periodicity; 4.2.2 Stability of periodic points; 4.2.3 Bifurcation; 4.2.4 Sarkovskii's theorem*; 4.2.5 Chaos and symbolic dynamics; Problems.
Text of Note
4.3 Examplification: Riffle shuffles and the shift map4.3.1 Riffle shuffles; 4.3.2 The shift map; 4.3.3 Shifting and shuffling; 4.3.4 Shuffling again and again; Problems; 5 Fractals; 5.1 Cantor's set; 5.1.1 Symbolic representation of Cantor's set; 5.1.2 Cantor's set in conventional notation; 5.1.3 The link between the two representations; 5.1.4 Topological properties of the Cantor set; 5.1.5 In what sense a fractal?; Problems; 5.2 Biting out the middle in the plane; 5.2.1 Sierpinski's triangle; 5.2.2 Koch's snowflake; Problems; 5.3 Contraction mapping theorems; 5.3.1 Contraction maps.
Text of Note
5.3.2 Contraction mapping theorem on the real line5.3.3 Contraction mapping in higher dimensions; 5.3.4 Contractive affine maps: the spectral norm*; 5.3.5 Other metric spaces; 5.3.6 Compact sets and Hausdorff distance; Problems; 5.4 Iterated function systems; 5.4.1 From point maps to set maps; 5.4.2 The union of set maps; 5.4.3 Examples revisited; 5.4.4 IFSs defined; 5.4.5 Working backward; Problems; 5.5 Algorithms for drawing fractals; 5.5.1 A deterministic algorithm; 5.5.2 Dancing on fractals; 5.5.3 A randomized algorithm; Problems; 5.6 Fractal dimension; 5.6.1 Covering with balls.
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SUMMARY OR ABSTRACT
Text of Note
This text is designed for those who wish to study mathematics beyond linear algebra but are not ready for abstract material. Rather than a theorem-proof-corollary-remark style of exposition, it stresses geometry, intuition, and dynamical systems. An appendix explains how to write MATLAB, Mathematica, and C programs to compute dynamical systems. 1996 edition.
OTHER EDITION IN ANOTHER MEDIUM
Title
Invitation to dynamical systems.
International Standard Book Number
9780486485942
TOPICAL NAME USED AS SUBJECT
Differentiable dynamical systems.
Differentiable dynamical systems.
MATHEMATICS-- Geometry-- Differential.
DEWEY DECIMAL CLASSIFICATION
Number
003/
.
85
Edition
23
LIBRARY OF CONGRESS CLASSIFICATION
Class number
QA614
.
8
Book number
.
S34
2012eb
PERSONAL NAME - PRIMARY RESPONSIBILITY
Scheinerman, Edward R.
ORIGINATING SOURCE
Date of Transaction
20200822114434.0
Cataloguing Rules (Descriptive Conventions))
pn
ELECTRONIC LOCATION AND ACCESS
Electronic name
مطالعه متن کتاب [Book]
Y
