skip to content
Chaos and fractals : an elementary introduction Preview this item
ClosePreview this item
Checking...

Chaos and fractals : an elementary introduction

Author: David P Feldman
Publisher: Oxford : Oxford University Press, 2012.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Database:WorldCat
Summary:
For students with a background in elementary algebra, this text provides a vivid introduction to the key phenomena and ideas of chaos and fractals, including the butterfly effect, strange attractors, fractal dimensions, Julia sets and the Mandelbrot set, power laws, and cellular automata.
Rating:

(not yet rated) 0 with reviews - Be the first.

Subjects
More like this

 

Find a copy online

Links to this item

Find a copy in the library

&AllPage.SpinnerRetrieving; Finding libraries that hold this item...

Details

Genre/Form: Electronic books
Additional Physical Format: Print version:
Feldman, David P.
Chaos and fractals.
Oxford : Oxford University Press, 2012
(OCoLC)792747080
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: David P Feldman
ISBN: 9780191637520 0191637521 6613956384 9786613956385 128364388X 9781283643887
OCLC Number: 812197926
Description: 1 online resource (xxi, 408 pages) : illustrations
Contents: Cover; Contents; I: Introducing Discrete Dynamical Systems; 0 Opening Remarks; 0.1 Chaos; 0.2 Fractals; 0.3 The Character of Chaos and Fractals; 1 Functions; 1.1 Functions as Actions; 1.2 Functions as a Formula; 1.3 Functions are Deterministic; 1.4 Functions as Graphs; 1.5 Functions as Maps; Exercises; 2 Iterating Functions; 2.1 The Idea of Iteration; 2.2 Some Vocabulary and Notation; 2.3 Iterated Function Notation; 2.4 Algebraic Expressions for Iterated Functions; 2.5 Why Iteration?; Exercises; 3 Qualitative Dynamics: The Fate of the Orbit; 3.1 Dynamical Systems. 3.2 Dynamics of the Squaring Function3.3 The Phase Line; 3.4 Fixed Points via Algebra; 3.5 Fixed Points Graphically; 3.6 Types of Fixed Points; Exercises; 4 Time Series Plots; 4.1 Examples of Time Series Plots; Exercises; 5 Graphical Iteration; 5.1 An Initial Example; 5.2 The Method of Graphical Iteration; 5.3 Further Examples; Exercises; 6 Iterating Linear Functions; 6.1 A Series of Examples; 6.2 Slopes of +1 or -1; Exercises; 7 Population Models; 7.1 Exponential Growth; 7.2 Modifying the Exponential Growth Model; 7.3 The Logistic Equation; 7.4 A Note on the Importance of Stability. 7.5 Other r ValuesExercises; 8 Newton, Laplace, and Determinism; 8.1 Newton and Universal Mechanics; 8.2 The Enlightenment and Optimism; 8.3 Causality and Laplace's Demon; 8.4 Science Today; 8.5 A Look Ahead; II: Chaos; 9 Chaos and the Logistic Equation; 9.1 Periodic Behavior; 9.2 Aperiodic Behavior; 9.3 Chaos Defined; 9.4 Implications of Aperiodic Behavior; Exercises; 10 The Butterfly Effect; 10.1 Stable Periodic Behavior; 10.2 Sensitive Dependence on Initial Conditions; 10.3 SDIC Defined; 10.4 Lyapunov Exponents; 10.5 Stretching and Folding: Ingredients for Chaos. 10.6 Chaotic Numerics: The Shadowing LemmaExercises; 11 The Bifurcation Diagram; 11.1 A Collection of Final-State Diagrams; 11.2 Periodic Windows; 11.3 Bifurcation Diagram Summary; Exercises; 12 Universality; 12.1 Bifurcation Diagrams for Other Functions; 12.2 Universality of Period Doubling; 12.3 Physical Consequences of Universality; 12.4 Renormalization and Universality; 12.5 How are Higher-Dimensional Phenomena Universal?; Exercises; 13 Statistical Stability of Chaos; 13.1 Histograms of Periodic Orbits; 13.2 Histograms of Chaotic Orbits; 13.3 Ergodicity; 13.4 Predictable Unpredictability. Exercises14 Determinism, Randomness, and Nonlinearity; 14.1 Symbolic Dynamics; 14.2 Chaotic Systems as Sources of Randomness; 14.3 Randomness?; 14.4 Linearity, Nonlinearity, and Reductionism; 14.5 Summary and a Look Ahead; Exercises; III: Fractals; 15 Introducing Fractals; 15.1 Shapes; 15.2 Self-Similarity; 15.3 Typical Size?; 15.4 Mathematical vs. Real Fractals; Exercises; 16 Dimensions; 16.1 How Many Little Things Fit inside a Big Thing?; 16.2 The Dimension of the Snowflake; 16.3 What does D {u2248} 1.46497 Mean?; 16.4 The Dimension of the Cantor Set; 16.5 The Dimension of the Sierpiński Triangle.
Responsibility: David P. Feldman.

Abstract:

For students with a background in elementary algebra, this book provides a vivid introduction to the key phenomena and ideas of chaos and fractals, including the butterfly effect, strange attractors,  Read more...

Reviews

Editorial reviews

Publisher Synopsis

[haos and Fractals] offers at least the possibility of a radically different trajectory for school teaching, providing a motivated pathway to a lot of fascinating mathematics not normally considered Read more...

 
User-contributed reviews
Retrieving GoodReads reviews...
Retrieving DOGObooks reviews...

Tags

Be the first.
Confirm this request

You may have already requested this item. Please select Ok if you would like to proceed with this request anyway.

Linked Data


Primary Entity

<http://www.worldcat.org/oclc/812197926> # Chaos and fractals : an elementary introduction
    a schema:MediaObject, schema:CreativeWork, schema:Book ;
   library:oclcnum "812197926" ;
   library:placeOfPublication <http://id.loc.gov/vocabulary/countries/enk> ;
   library:placeOfPublication <http://experiment.worldcat.org/entity/work/data/1106193987#Place/oxford> ; # Oxford
   schema:about <http://id.worldcat.org/fast/933507> ; # Fractals
   schema:about <http://dewey.info/class/514.742/e23/> ;
   schema:about <http://id.worldcat.org/fast/852171> ; # Chaotic behavior in systems
   schema:about <http://experiment.worldcat.org/entity/work/data/1106193987#Topic/mathematics_topology> ; # MATHEMATICS--Topology
   schema:bookFormat schema:EBook ;
   schema:creator <http://viaf.org/viaf/264993410> ; # David P. Feldman
   schema:datePublished "2012" ;
   schema:description "Cover; Contents; I: Introducing Discrete Dynamical Systems; 0 Opening Remarks; 0.1 Chaos; 0.2 Fractals; 0.3 The Character of Chaos and Fractals; 1 Functions; 1.1 Functions as Actions; 1.2 Functions as a Formula; 1.3 Functions are Deterministic; 1.4 Functions as Graphs; 1.5 Functions as Maps; Exercises; 2 Iterating Functions; 2.1 The Idea of Iteration; 2.2 Some Vocabulary and Notation; 2.3 Iterated Function Notation; 2.4 Algebraic Expressions for Iterated Functions; 2.5 Why Iteration?; Exercises; 3 Qualitative Dynamics: The Fate of the Orbit; 3.1 Dynamical Systems."@en ;
   schema:description "For students with a background in elementary algebra, this text provides a vivid introduction to the key phenomena and ideas of chaos and fractals, including the butterfly effect, strange attractors, fractal dimensions, Julia sets and the Mandelbrot set, power laws, and cellular automata."@en ;
   schema:exampleOfWork <http://worldcat.org/entity/work/id/1106193987> ;
   schema:genre "Electronic books"@en ;
   schema:inLanguage "en" ;
   schema:isSimilarTo <http://www.worldcat.org/oclc/792747080> ;
   schema:name "Chaos and fractals : an elementary introduction"@en ;
   schema:productID "812197926" ;
   schema:publication <http://www.worldcat.org/title/-/oclc/812197926#PublicationEvent/oxford_oxford_university_press_2012> ;
   schema:publisher <http://experiment.worldcat.org/entity/work/data/1106193987#Agent/oxford_university_press> ; # Oxford University Press
   schema:url <http://ebookcentral.proquest.com/lib/oldscollege/detail.action?docID=1043133> ;
   schema:url <https://ezproxy.kpu.ca:2443/login?url=http://site.ebrary.com/lib/kwantlen/Doc?id=10610326> ;
   schema:url <http://ebookcentral.proquest.com/lib/concordiaab-ebooks/detail.action?docID=1043133> ;
   schema:url <http://ebookcentral.proquest.com/lib/stanford-ebooks/detail.action?docID=1043133> ;
   schema:url <http://libweb.ben.edu/login?url=http://site.ebrary.com/lib/benu/Doc?id=10610326> ;
   schema:url <http://ebookcentral.proquest.com/lib/soas-ebooks/detail.action?docID=1043133> ;
   schema:url <http://ebookcentral.proquest.com/lib/rdc/detail.action?docID=1043133> ;
   schema:url <http://proxy.ufv.ca:2048/login?url=http://site.ebrary.com/lib/ucfv/Doc?id=10610326> ;
   schema:url <http://dx.doi.org/10.1093/acprof:oso/9780199566433.001.0001> ;
   schema:url <http://ebookcentral.proquest.com/lib/macewan-ebooks/detail.action?docID=1043133> ;
   schema:url <http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=490093> ;
   schema:url <http://site.ebrary.com/lib/interpuertorico/Doc?id=10610326> ;
   schema:url <http://www.myilibrary.com?id=395638> ;
   schema:url <http://ebookcentral.proquest.com/lib/gprc-ebooks/detail.action?docID=1043133> ;
   schema:url <http://ebookcentral.proquest.com/lib/ucm/detail.action?docID=1043133> ;
   schema:url <http://er.llcc.edu:2048/login?url=http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=490093> ;
   schema:url <http://public.eblib.com/choice/publicfullrecord.aspx?p=1043133> ;
   schema:url <http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=e000xna&AN=490093> ;
   schema:url <http://ebookcentral.proquest.com/lib/norquest-ebooks/detail.action?docID=1043133> ;
   schema:url <http://www.myilibrary.com?id=395638&ref=toc> ;
   schema:url <http://site.ebrary.com/id/10610326> ;
   schema:url <http://site.ebrary.com/lib/ucmerced/Top?id=10610326> ;
   schema:workExample <http://worldcat.org/isbn/9786613956385> ;
   schema:workExample <http://worldcat.org/isbn/9781283643887> ;
   schema:workExample <http://worldcat.org/isbn/9780191637520> ;
   wdrs:describedby <http://www.worldcat.org/title/-/oclc/812197926> ;
    .


Related Entities

<http://ebookcentral.proquest.com/lib/concordiaab-ebooks/detail.action?docID=1043133>
   rdfs:comment "from Ebook Central Academic Complete" ;
   rdfs:comment "(Unlimited Concurrent Users)" ;
    .

<http://ebookcentral.proquest.com/lib/gprc-ebooks/detail.action?docID=1043133>
   rdfs:comment "from Ebook Central Academic Complete" ;
   rdfs:comment "(Unlimited Concurrent Users)" ;
    .

<http://ebookcentral.proquest.com/lib/macewan-ebooks/detail.action?docID=1043133>
   rdfs:comment "from Ebook Central Academic Complete" ;
   rdfs:comment "(Unlimited Concurrent Users)" ;
    .

<http://ebookcentral.proquest.com/lib/rdc/detail.action?docID=1043133>
   rdfs:comment "from Ebook Central Academic Complete" ;
   rdfs:comment "(Unlimited Concurrent Users)" ;
    .

<http://ebookcentral.proquest.com/lib/soas-ebooks/detail.action?docID=1043133>
   rdfs:comment "Connect to electronic book via Ebook Central." ;
    .

<http://experiment.worldcat.org/entity/work/data/1106193987#Agent/oxford_university_press> # Oxford University Press
    a bgn:Agent ;
   schema:name "Oxford University Press" ;
    .

<http://experiment.worldcat.org/entity/work/data/1106193987#Topic/mathematics_topology> # MATHEMATICS--Topology
    a schema:Intangible ;
   schema:name "MATHEMATICS--Topology"@en ;
    .

<http://id.worldcat.org/fast/852171> # Chaotic behavior in systems
    a schema:Intangible ;
   schema:name "Chaotic behavior in systems"@en ;
    .

<http://id.worldcat.org/fast/933507> # Fractals
    a schema:Intangible ;
   schema:name "Fractals"@en ;
    .

<http://libweb.ben.edu/login?url=http://site.ebrary.com/lib/benu/Doc?id=10610326>
   rdfs:comment "(access limited to Benedictine University patrons)" ;
    .

<http://proxy.ufv.ca:2048/login?url=http://site.ebrary.com/lib/ucfv/Doc?id=10610326>
   rdfs:comment "An electronic book accessible through the World Wide Web; click to view" ;
    .

<http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=e000xna&AN=490093>
   rdfs:comment "from EBSCO Academic Collection" ;
   rdfs:comment "(Unlimited Concurrent Users)" ;
    .

<http://site.ebrary.com/lib/interpuertorico/Doc?id=10610326>
   rdfs:comment "An electronic book accessible through the World Wide Web; click to view" ;
    .

<http://viaf.org/viaf/264993410> # David P. Feldman
    a schema:Person ;
   schema:familyName "Feldman" ;
   schema:givenName "David P." ;
   schema:name "David P. Feldman" ;
    .

<http://worldcat.org/isbn/9780191637520>
    a schema:ProductModel ;
   schema:isbn "0191637521" ;
   schema:isbn "9780191637520" ;
    .

<http://worldcat.org/isbn/9781283643887>
    a schema:ProductModel ;
   schema:isbn "128364388X" ;
   schema:isbn "9781283643887" ;
    .

<http://worldcat.org/isbn/9786613956385>
    a schema:ProductModel ;
   schema:isbn "6613956384" ;
   schema:isbn "9786613956385" ;
    .

<http://www.worldcat.org/oclc/792747080>
    a schema:CreativeWork ;
   rdfs:label "Chaos and fractals." ;
   schema:description "Print version:" ;
   schema:isSimilarTo <http://www.worldcat.org/oclc/812197926> ; # Chaos and fractals : an elementary introduction
    .

<https://ezproxy.kpu.ca:2443/login?url=http://site.ebrary.com/lib/kwantlen/Doc?id=10610326>
   rdfs:comment "An electronic book accessible through the World Wide Web; click to view" ;
    .


Content-negotiable representations

Close Window

Please sign in to WorldCat 

Don't have an account? You can easily create a free account.