Discovering Dynamical Systems Through Experiment and Inquiry
暫譯: 透過實驗與探究發現動態系統

Lofaro, Thomas, Ford, Jeff

Discovering Dynamical Systems Through Experiment and Inquiry
  • 出版商: CRC
  • 出版日期: 2021-03-23
  • 售價: $4,110
  • 貴賓價: 9.5 折 $3,905
  • 語言: 英文
  • 頁數: 215
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 0367903946
  • ISBN-13: 9780367903947

    • 海外代購書籍(需單獨結帳)

相關主題

商品描述

Discovering Dynamical Systems Through Experiment and Inquiry differs from most texts on dynamical systems by blending the use of computer simulations with inquiry-based learning (IBL). IBL is an excellent tool to move students from merely remembering the material to deeper understanding and analysis. This method relies on asking students questions first, rather than presenting the material in a lecture.

Another unique feature of this book is the use of computer simulations. Students can discover examples and counterexamples through manipulations built into the software. These tools have long been used in the study of dynamical systems to visualize chaotic behavior.

We refer to this unique approach to teaching mathematics as ECAP--Explore, Conjecture, Apply, and Prove. ECAP was developed to mimic the actual practice of mathematics in an effort to provide students with a more holistic mathematical experience. In general, each section begins with exercises guiding students through explorations of the featured concept and concludes with exercises that help the students formally prove the results.

While symbolic dynamics is a standard topic in an undergraduate dynamics text, we have tried to emphasize it in a way that is more detailed and inclusive than is typically the case. Finally, we have chosen to include multiple sections on important ideas from analysis and topology independent from their application to dynamics.

商品描述(中文翻譯)

《透過實驗與探究發現動態系統》與大多數動態系統的教材不同，因為它將電腦模擬與探究式學習（Inquiry-Based Learning, IBL）結合在一起。IBL是一種優秀的工具，可以幫助學生從單純記憶材料轉向更深入的理解與分析。這種方法依賴於先向學生提出問題，而不是在講座中直接呈現材料。

本書的另一個獨特特點是使用電腦模擬。學生可以通過內建於軟體中的操作來發現例子和反例。這些工具在動態系統的研究中已被廣泛用來可視化混沌行為。

我們將這種獨特的數學教學方法稱為ECAP——探索（Explore）、猜想（Conjecture）、應用（Apply）和證明（Prove）。ECAP的發展旨在模擬數學的實際實踐，以便為學生提供更全面的數學體驗。一般來說，每個章節都以引導學生探索所介紹概念的練習開始，並以幫助學生正式證明結果的練習結束。

雖然符號動力學是本科動力學教材中的標準主題，但我們試圖以比通常情況更詳細和包容的方式來強調它。最後，我們選擇包含多個獨立於其在動力學應用的分析和拓撲學重要概念的部分。

作者簡介

Tom LoFaro: Tom LoFaro is the Clifford M. Swanson Professor of Mathematics at Gustavus Adolphus College. He earned his Bachelor's and Master's degrees in mathematics from the University of Missouri. He then earned his Ph.D. from Boston University in mathematics under the direction of Nancy Kopell. Tom's research interests are in the applications of dynamical systems to mathematical biology in general and neuroscience in particular and is an Affiliated Faculty Member of the Institute for the Study of Decision Making at New York University. Tom has been active in the differential equations and dynamical systems education community and in the past worked closely with the Community for Ordinary Differential Equations Educators where he has published several articles their journal. Jeff Ford: Jeff Ford is a Visiting Assistant Professor of Mathematics at Gustavus Adolphus College. He earned his Bachelor's degree from Gustavus Adolphus College, his Master's degree in mathematics from Minnesota State University - Mankato, and his Ph.D. in mathematics from Auburn University, studying under Dr. Krystyna Kuperberg. Jeff is interested in the existence volume-preserving dynamical systems with unique properties. Jeff uses and assesses a variety of active learning techniques in his class including inquiry-based learning and team-based learning. His scholarship in this area centers on understanding how active learning techniques improve confidence and reduce anxiety in undergraduate students.

作者簡介(中文翻譯)

湯姆·洛法羅（Tom LoFaro）：湯姆·洛法羅是古斯塔夫·阿道夫學院（Gustavus Adolphus College）數學的克利福德·M·斯旺森教授。他在密蘇里大學（University of Missouri）獲得數學的學士和碩士學位，隨後在波士頓大學（Boston University）獲得數學博士學位，指導教授為南希·科佩爾（Nancy Kopell）。湯姆的研究興趣在於動態系統在數學生物學（mathematical biology）中的應用，特別是神經科學（neuroscience），並且是紐約大學（New York University）決策研究所（Institute for the Study of Decision Making）的附屬教員。湯姆在微分方程和動態系統教育社群中非常活躍，過去曾與普通微分方程教育者社群（Community for Ordinary Differential Equations Educators）密切合作，並在他們的期刊上發表了幾篇文章。

傑夫·福特（Jeff Ford）：傑夫·福特是古斯塔夫·阿道夫學院的訪問助理教授（Visiting Assistant Professor）數學。他在古斯塔夫·阿道夫學院獲得學士學位，在明尼蘇達州立大學-曼卡托（Minnesota State University - Mankato）獲得數學碩士學位，並在奧本大學（Auburn University）獲得數學博士學位，指導教授為克里斯蒂娜·庫佩爾伯格（Dr. Krystyna Kuperberg）。傑夫對於存在具有獨特性質的體積守恆動態系統（volume-preserving dynamical systems）感興趣。傑夫在課堂上使用並評估各種主動學習技術，包括探究式學習（inquiry-based learning）和團隊學習（team-based learning）。他在這方面的學術研究集中於理解主動學習技術如何提高大學生的自信心並減少焦慮。

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