Fractional Calculus for Skeptics II: Quantifying Roughness
暫譯: 懷疑者的分數微積分 II：量化粗糙度

West, Bruce J., Chen, Yangquan

Fractional Calculus for Skeptics II: Quantifying Roughness
  • 出版商: CRC
  • 出版日期: 2026-03-25
  • 售價: $8,560
  • 貴賓價: 9.5 折 $8,132
  • 語言: 英文
  • 頁數: 150
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 1041171188
  • ISBN-13: 9781041171188
  • 相關分類: 工程數學 Engineering-mathematics

    • 海外代購書籍(需單獨結帳)

相關主題

商品描述

This second volume of the multi-volume Fractional Calculus for Skeptics explores the concept of "roughness" and its applications in complex systems. It demonstrates how fractional calculus offers valuable insights into modeling real-world phenomena that traditional calculus struggles to address.

Building on the first volume's foundational work advocating a fractal/fractional calculus paradigm shift, this volume offers an in-depth exploration of the concept of "roughness," drawing parallels to what Benoît B. Mandelbrot originally intended to call the "Science of Roughness." The book introduces the novel concept of "body roughness" and demonstrates its practical applications through two case studies of "roughness-informed rehabilitation therapy" with closed-loop control systems. One study involves non-invasive, 40-Hz gamma-frequency sensory stimulation for Alzheimer's disease, and the other involves biologically variable ventilation using roughness-informed, closed-loop control. The four chapters are complemented by valuable appendices and essential chapter-end references, as well as insightful "take-home messages."

This book will appeal to students, researchers, and professionals in STEM fields, including engineering, physics, biology, biomedicine, control engineering, rehabilitation, big data, and machine learning.

商品描述(中文翻譯)

這本多卷本《懷疑者的分數微積分》第二卷探討了「粗糙性」的概念及其在複雜系統中的應用。它展示了分數微積分如何提供對於建模現實世界現象的寶貴見解，而這些現象是傳統微積分難以處理的。

本卷在第一卷倡導的分形/分數微積分範式轉變的基礎上，深入探討了「粗糙性」的概念，並與貝努瓦·B·曼德布羅特（Benoît B. Mandelbrot）最初所稱的「粗糙科學」進行類比。書中引入了「身體粗糙性」的全新概念，並通過兩個「粗糙性知情的康復治療」案例研究展示其實際應用，這些案例使用了閉環控制系統。一個研究涉及對阿茲海默症的非侵入性、40赫茲伽瑪頻率感官刺激，另一個則涉及使用粗糙性知情的閉環控制進行生物變化通風。四個章節附有有價值的附錄和重要的章末參考資料，以及深刻的「帶回家的信息」。

這本書將吸引STEM領域的學生、研究人員和專業人士，包括工程學、物理學、生物學、生物醫學、控制工程、康復、大數據和機器學習等領域。

作者簡介

Bruce J. West, a Physics PhD from the University of Rochester 1970, was the Chief Scientist in Mathematical and Information Science at the Army Research Office of the US, 1999-2021. His awards include the Presidential Meritorious Rank Award 2012 (Obama) and the Presidential Distinguished Rank Award 2017 (Trump).

YangQuan Chen, a Clarivate Highly Cited Researcher, earned his Ph.D. from Nanyang Technological University, Singapore, in 1998. He is a professor at the School of Engineering, University of California, Merced. His research interests include smart control engineering via digital twins and applied fractional calculus in STEM.

作者簡介(中文翻譯)

布魯斯·J·韋斯特（Bruce J. West），1970年獲得羅切斯特大學（University of Rochester）物理學博士，曾於1999年至2021年擔任美國陸軍研究辦公室（Army Research Office）數學與資訊科學首席科學家。他的獎項包括2012年（歐巴馬）頒發的總統優異等級獎（Presidential Meritorious Rank Award）和2017年（特朗普）頒發的總統傑出等級獎（Presidential Distinguished Rank Award）。

陳揚全（YangQuan Chen），為Clarivate高被引研究者，1998年在新加坡南洋理工大學（Nanyang Technological University）獲得博士學位。他是加州大學默塞德分校（University of California, Merced）工程學院的教授。他的研究興趣包括透過數位雙胞胎（digital twins）進行智慧控制工程以及在STEM領域應用分數微積分（fractional calculus）。

類似商品