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Nonlinear Dynamics And Chaos: With Applications To Physics, Biology, Chemistry, And Engineering (Studies in nonlinearity)
 
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Nonlinear Dynamics And Chaos: With Applications To Physics, Biology, Chemistry, And Engineering (Studies in nonlinearity) (ペーパーバック)

by Steven H. Strogatz (著)
5.0 out of 5 stars  See all reviews (2 customer reviews)
Price: ￥ 5,243 (Tax Included) & eligible for Free Shipping. Details
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Product Description

内容説明

This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors.A unique feature of the book is its emphasis on applications. These include mechanical vibrations, lasers, biological rhythms, superconducting circuits, insect outbreaks, chemical oscillators, genetic control systems, chaotic waterwheels, and even a technique for using chaos to send secret messages. In each case, the scientific background is explained at an elementary level and closely integrated with the mathematical theory.Richly illustrated, and with many exercises and worked examples, this book is ideal for an introductory course at the junior/senior or first-year graduate level. It is also ideal for the scientist who has not had formal instruction in nonlinear dynamics, but who now desires to begin informal study. The prerequisites are multivariable calculus and introductory physics.

Product Details

  • ペーパーバック: 512 pages
  • Publisher: Westview Press; illustrated edition edition (2001/1/15)
  • Language: 英語, 英語, 英語
  • ISBN-10: 0738204536
  • ISBN-13: 978-0738204536
  • Release Date: 2001/1/15
  • Product Dimensions: 9.2 x 6 x 1.1 inches
  • Average Customer Review: 5.0 out of 5 stars  See all reviews (2 customer reviews)
  • Amazon.co.jp Sales Rank: #20,624 in 洋書 (See Bestsellers in 洋書)

    Popular in these categories:

    #29 in  洋書 > Science > Physics > Chaos & Systems
    #49 in  洋書 > Science > Mathematics > Pure Mathematics > Calculus
    #80 in  洋書 > Medical > Basic Sciences > Biology

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5.0 out of 5 stars (2 customer reviews)
 
 
 
 
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5 of 5 people found the following review helpful:
5.0 out of 5 stars カオスではなく非線形力学の入門書としておすすめ, 2006/11/4
Nonlinear Dynamics and Chaosという題名の本は数多くあれど，この本ほど親切丁寧な本はないだろう．大抵，カオスを語った本というのは（特に和書）筆者自身がどうしても"カオス"を語りたがるものらしく，基本そっちのけでさっさと複雑系の話に流れてしまう．

この本は３パートに分かれている．パート１で１次元系の流れ．パート２で２次元系の線形システムと非線形システム．パート３がカオスである．それぞれ100ページほど割り当てられており，非線形力学の教科書としては２パート目までで十分であろう．だいたいカオスは趣味でやるものであって，工学者にとっては２次元系の非線形力学の手法がわかれば十分である．その点に於いてこの教科書は"わかっている"．

各システムの解説ではできるだけ具体例を用いて説明してくれるため直感的に理解しやすい．「具体例を用いて」とは，ホタルの発光現象や超電導接合など自然界の具体例を持ち出してきてモデル化するところから説明が始まるという意味である．読めば分かるように丁寧に書いてある点も評価が高い（信じられないことに，世の中読んでも分からない本が多い(特に和書)）．例題や章末問題も豊富なため授業に使ってもいいだろう．英文は簡潔かつ丁寧．学部・修士レベルの初心者向け教科書として我が研究室では重宝している．

残念なことに欠点が１つだけある．
Strogatz先生にはどうもシャレのセンスがないようだ．
２次元線形システムの例として丸々１節を割いてでてくるLove Affairなどはどうしたものか．毎年この節に達すると室内温度が低下する．
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2 of 2 people found the following review helpful:
5.0 out of 5 stars 力学系の扉を開くための基本図書, 2008/7/6
By 一力学系ファン (愛媛県松山市) - See all my reviews
　私は５０代の一社会人ですが，趣味として「力学系」を学んでいます．独学のため，本が学習の拠り所となっています．数年前，たまたまブックリストで本書を見つけて買っていたのですが，その後いろいろな所で，非常にいい本であると紹介されていたため，まともに読んでみました．
　私のような，研究者でも学生でもない，半素人のいわば第３の立場からの感想です．通常の解説書では，概略はなんとなくわかっても，さらに理解を深めようとすれば壁に当たってしまいます．本書は基本的な概念の内容を，数学書の基本スタイルである，定義・定理で構成していく方法をとらず，簡潔な説明とその内容を表現する典型例で理解させるという形態になっています．これが初心者には非常にわかりやすい．しかも，前で上げた例が，後でさらなる役割を果たすように，周到に配列されていることを感じます．もう一点は練習問題です．通常，問題を解くときになると，初学者には本文の理解と問題の程度にギャップがあり，解き方の見当が皆目つかないことになりがちです．そこのところを本書は，手がかりを与えてうまく誘導してくれるように思います．本書はMITやコーネル大学の学部生用の教科書として，使われたようですが（同じ著者のSYNCという本に，この本のことについての学生の感想が出てきます），このスタイルは，私のような独学者にも学習をあきらめさせずに，次の学習に向かう意欲を与えてくれます．
　もちろん，一方でこの形式は力学系の学習の入り口として有効ですが，欠点でもあると思います．内容の数学的な厳密性や証明は，他書で補わなければなりません．例えば，節か章の最後に，重要なものについてのきちんとした証明をつけてもらえば，self-containedになって良かったのにと思います．
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