Generating Functions in Engineering and the Applied Sciences

Chattamvelli, Rajan, Shanmugam, Ramalingam

  • 出版商: Springer
  • 出版日期: 2023-01-02
  • 售價: $2,000
  • 貴賓價: 9.5$1,900
  • 語言: 英文
  • 頁數: 119
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 3031211421
  • ISBN-13: 9783031211423
  • 相關分類: 工程數學 Engineering-mathematics
  • 海外代購書籍(需單獨結帳)

商品描述

Generating function (GF) is a mathematical technique to concisely represent a known ordered sequence into a simple continuous algebraic function in dummy variable(s). This Second Edition introduces commonly encountered generating functions (GFs) in engineering and applied sciences, such as ordinary GF (OGF), exponential GF (EGF), as also Dirichlet GF (DGF), Lambert GF (LGF), Logarithmic GF (LogGF), Hurwitz GF (HGF), Mittag-Lefler GF (MLGF), etc. This book is intended mainly for beginners in applied science and engineering fields to help them understand single-variable GFs and illustrate how to apply them in various practical problems. Specifically, the book discusses probability GFs (PGF), moment and cumulant GFs (MGF, CGF), mean deviation GFs (MDGF), survival function GFs (SFGF), rising and falling factorial GFs, factorial moment, and inverse factorial moment GFs. Applications of GFs in algebra, analysis of algorithms, bioinformatics, combinatorics, economics, finance, genomics, geometry, graph theory, management, number theory, polymer chemistry, reliability, statistics and structural engineering have been added to this new edition. This book is written in such a way that readers who do not have prior knowledge of the topic can easily follow through the chapters and apply the lessons learned in their respective disciplines.

商品描述(中文翻譯)

生成函數(GF)是一種數學技巧,將已知的有序序列簡潔地表示為一個或多個虛擬變量的簡單連續代數函數。這本第二版介紹了在工程和應用科學中常見的生成函數(GF),例如普通生成函數(OGF)、指數生成函數(EGF)、迪利克雷生成函數(DGF)、蘭伯特生成函數(LGF)、對數生成函數(LogGF)、赫爾維茨生成函數(HGF)、米塔格-勒弗勒生成函數(MLGF)等。本書主要針對應用科學和工程領域的初學者,幫助他們理解單變量生成函數,並說明如何應用於各種實際問題。具體而言,本書討論了概率生成函數(PGF)、矩和累積生成函數(MGF、CGF)、平均偏差生成函數(MDGF)、生存函數生成函數(SFGF)、上升和下降階乘生成函數、階乘矩和倒數階乘矩生成函數。本版新增了生成函數在代數、算法分析、生物信息學、組合學、經濟學、金融學、基因組學、幾何學、圖論、管理學、數論、高分子化學、可靠性、統計學和結構工程學中的應用。本書以讀者無需先備知識為前提,易於理解各章節的內容,並能將所學應用於相應的學科領域。

作者簡介

Rajan Chattamvelli, Ph.D., is a Professor in the School of Advanced Sciences at Vellore Institute of Technology, Tamil Nadu, India. He has published more than 20 research articles in international journals, and his research interests include computational statistics, design of algorithms, parallel computing, data mining, machine learning, blockchain, combinatorics, and big data analytics.
Ramalingam Shanmugam, Ph.D., is an Honorary Professor in the School of Health Administration at Texas State University, San Marcos. He is the Editor-in-Chief of four journals including Advances in Life Sciences; Global Journal of Research and Review; Journal of Obesity and Metabolism; and the International Journal of Research in Medical Sciences. He has published more than 200 research articles and 120 conference papers. Dr. Shanmugam's research interests include theoretical and computational statistics, number theory, operations research, biostatistics, decision making, and epidemiology.


作者簡介(中文翻譯)

Rajan Chattamvelli博士是印度泰米爾納德邦Vellore理工學院高級科學學院的教授。他在國際期刊上發表了20多篇研究論文,他的研究興趣包括計算統計學、算法設計、並行計算、數據挖掘、機器學習、區塊鏈、組合數學和大數據分析。

Ramalingam Shanmugam博士是德克薩斯州立大學聖馬科斯分校健康管理學院的名譽教授。他是四本期刊的主編,包括《生命科學進展》、《全球研究與評論期刊》、《肥胖與代謝期刊》和《醫學科學研究國際期刊》。他發表了200多篇研究論文和120篇會議論文。Shanmugam博士的研究興趣包括理論和計算統計學、數論、運籌學、生物統計學、決策分析和流行病學。