Fractional Calculus: High-Precision Algorithms and Numerical Implementations

Xue, Dingyü, Bai, Lu

Fractional Calculus: High-Precision Algorithms and Numerical Implementations
  • 出版商: Springer
  • 出版日期: 2024-05-04
  • 售價: $6,460
  • 貴賓價: 9.5 折 $6,137
  • 語言: 英文
  • 頁數: 409
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 9819920698
  • ISBN-13: 9789819920693
  • 相關分類: 微積分 Calculus、Algorithms-data-structures

    • 海外代購書籍(需單獨結帳)

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商品描述

Fractional calculus and its applications are fascinating research areas in many engineering disciplines. This book is a comprehensive collection of research from the author's group, which is one of the most active in the fractional calculus community worldwide and is the birthplace of one of the four MATLAB toolboxes in fractional calculus, the FOTF Toolbox. The book presents high-precision solution algorithms for a variety of fractional-order differential equations, including nonlinear, delay, and boundary value equations. Currently, there are no other universal solvers available for the latter two types of equations.

Through this book, readers can systematically study the mathematics and solution methods in the field of fractional calculus and apply these concepts to different engineering fields, particularly control systems engineering.

This book is a translation of an original German edition. The translation was done with the help of artificial intelligence (machine translation by the service DeepL.com). A subsequent human revision was done primarily in terms of content, so that the book will read stylistically differently from a conventional translation.

商品描述(中文翻譯)

分數微積分及其應用是許多工程學科中引人入勝的研究領域。本書是作者團隊的綜合研究成果，該團隊是全球分數微積分社群中最活躍的之一，也是分數微積分 MATLAB 工具箱之一，即 FOTF Toolbox 的誕生地。本書介紹了各種分數階微分方程的高精度解算法，包括非線性、時滯和邊界值方程。目前，對於後兩種方程類型，沒有其他通用求解器可用。

通過本書，讀者可以系統地學習分數微積分領域的數學和解法方法，並將這些概念應用於不同的工程領域，特別是控制系統工程。

本書是原始德文版的翻譯。翻譯是通過人工智能（由 DeepL.com 提供的機器翻譯）完成的。隨後進行了人工修訂，主要是在內容方面，因此本書在風格上與傳統翻譯有所不同。

作者簡介

Xue Dingyu, received his doctorate from Sussex University in 1992, and took his post at Northeastern University in China in 1993, where he was promoted to full professorship in 1997. He started his teaching work on MATLAB since 1990, where he designed a Lab Demonstration GUI for Classroom in Sussex University, while he we doing his D Phil research. In 1996, he published his first MATLAB book in Chinese, entitled "Computer aided Control System Design with MATLAB Applications" in Tsinghua University Press in China, which was regarded the first in China, and one of the first few earliest ones in the world. In 30+ years of time, he has published 12 books in English plus numerous books in Chinese. The recent ones are the six-volume works on scientific computing and simulation, published in De Gruyter, Berlin, in 2020-2022.

He received many teaching honors and awards in China, for National-level Elite Courses, Textbooks, and National First-class Undergraduate courses, and national-level Educational Awards. He is the co-founder and vice-chair of the Fractional-order Systems and Control Committee, China Automation Association. He received two China Natural Science Foundation grants on fractional systems. Co-author (4th) of the 2010 Springer monograph on fractional calculus, Author of the 2017 De Gruyter monograph on Fractional calculus and fractional-order control. He is the author of the FOTF MATLAB Toolbox, one of the four most widely used MATLAB tools in the fractional calculus community worldwide.

Bai Lu, was a PhD candidate under Xue Dingyu's supervision. He received his doctorate from Northeastern University in 2018, with many contributions in high-precision algorithms. He is now a lecturer in Shenyang University. He is also the co-author of the Chinese version of the proposed monograph.

作者簡介(中文翻譯)

薛定宇於1992年在薩塞克斯大學獲得博士學位，並於1993年在中國東北大學任職，於1997年晉升為正教授。他自1990年開始教授MATLAB，當時他在薩塞克斯大學進行D Phil研究時，設計了一個用於課堂的實驗室演示GUI。1996年，他在中國清華大學出版了他的第一本MATLAB書籍，名為《基於MATLAB的計算機輔助控制系統設計》，被認為是中國的第一本，也是世界上最早的幾本之一。在30多年的時間裡，他出版了12本英文書籍和眾多中文書籍。最近的作品是2020-2022年在德國德古意特出版社出版的六卷本科學計算和模擬作品。

他在中國獲得了許多教學榮譽和獎項，包括國家級精品課程、教材和國家一流本科課程以及國家級教育獎項。他是中國自動化學會分數階系統與控制委員會的聯合創始人和副主席。他獲得了兩項中國自然科學基金會關於分數系統的資助。他是2010年Springer分數微積分專著的合著者（第四位），以及2017年De Gruyter分數微積分和分數階控制專著的作者。他是FOTF MATLAB工具箱的作者，該工具箱是全球分數微積分社區中使用最廣泛的四個MATLAB工具之一。

白璐是薛定宇的博士候選人，於2018年在東北大學獲得博士學位，對高精度算法做出了許多貢獻。他現在是瀋陽大學的講師，也是該提案中文版的合著者。

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