Modelling with Ordinary Differential Equations: A Comprehensive Approach
暫譯: 常微分方程式建模：完整解析
Borzì, Alfio
- 出版商: CRC
- 出版日期: 2026-11-03
- 售價: $8,240
- 貴賓價: 9.5 折 $7,828
- 語言: 英文
- 頁數: 502
- 裝訂: Hardcover - also called cloth, retail trade, or trade
- ISBN: 1032894245
- ISBN-13: 9781032894249
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相關分類:
數值分析 Numerical-analysis
海外代購書籍(需單獨結帳)
相關主題
商品描述
"Alfio Borzì's Modelling with Ordinary Differential Equations is a remarkably comprehensive text that succeeds in something rare: it covers the classical foundations of ODE theory with precision and rigour, while consistently opening windows to advanced and genuinely original applications that are hard to find in comparable textbooks"
--Professor Volker Schulz, Universität Trier
"Expertly written, organized and presented, Modelling with Ordinary Differential Equations: A Comprehensive Approach is an ideal textbook for college and university Numerical Analysis & Scientific Computing curriculums. [. . . ] unreservedly recommended as a critically important addition to academic library collections"
--Midwest Book Review
Modelling with Ordinary Differential Equations: A Comprehensive Approach aims to provide a broad and self-contained introduction to the mathematical tools necessary to investigate and apply ODE models. The book starts by establishing the existence of solutions in various settings and analysing their stability properties. The next step is to illustrate modelling issues arising in the calculus of variation and optimal control theory that are of interest in many applications. This discussion is continued with an introduction to inverse problems governed by ODE models and to differential games.
The book is completed with an illustration of stochastic differential equations and the development of neural networks to solve ODE systems. Many numerical methods are presented to solve the classes of problems discussed in this book.
New to the Second Edition:
This second edition has been thoroughly revised, reorganised, and expanded with new material across most chapters. The theoretical foundations are strengthened by additional results on existence and uniqueness, Lipschitz conditions, blow-up phenomena, and Green functions, as well as new sections on compartment models and Hamiltonian systems. A major addition is a new chapter on mechanics, ranging from classical to relativistic and quantum frameworks. The numerical analysis part now includes the Verlet method, while stability theory has been extended to cover chaos and synchronization.
Optimal control is treated in greater depth, with new material on the HJB equation, controllability, and free-horizon problems. Further additions include evolutionary differential games and enhanced inverse problem examples.The chapter on neural networks has been also expanded, introducing residual networks, and reservoir computing for dynamical systems.
商品描述(中文翻譯)
「Alfio Borzì 的《Modelling with Ordinary Differential Equations》是一本內容極為全面的著作，難得的是：本書以精確且嚴謹的方式涵蓋 ODE 理論的古典基礎，同時持續延伸至進階且真正具有原創性的應用，而這些內容在同類型教科書中相當少見。」
--Volker Schulz 教授，Trier 大學
「《Modelling with Ordinary Differential Equations: A Comprehensive Approach》撰寫、編排與呈現方式都極為出色，是大專院校數值分析（Numerical Analysis）與科學計算（Scientific Computing）課程的理想教科書。［……］本書無疑值得推薦，並且是學術圖書館館藏中至關重要的新增書籍。」
--《Midwest Book Review》
《Modelling with Ordinary Differential Equations: A Comprehensive Approach》旨在廣泛且完整地介紹研究與應用 ODE 模型所需的數學工具。本書首先在各種情境下建立解的存在性，並分析解的穩定性質。接著，說明變分法（calculus of variations）與最佳控制理論（optimal control theory）中所產生的建模問題；這些問題在許多應用領域都相當重要。之後，本書進一步介紹由 ODE 模型所支配的反問題（inverse problems），以及微分賽局（differential games）。
本書最後介紹隨機微分方程（stochastic differential equations），以及利用類神經網路（neural networks）求解 ODE 系統的方法。此外，書中也呈現許多數值方法，用於求解本書所討論的各類問題。
第二版新增內容：
本版經過全面修訂、重新編排，並在大多數章節中擴充了新內容。理論基礎透過增加存在性與唯一性、Lipschitz 條件、爆破解（blow-up phenomena）及 Green 函數等主題的結果而獲得強化；同時新增了區室模型（compartment models）與 Hamiltonian 系統的章節。一項重大新增內容是全新的一章「力學」，涵蓋從古典力學到相對論與量子力學的架構。數值分析部分現已納入 Verlet 方法，而穩定性理論也擴充至混沌（chaos）與同步（synchronization）。
最佳控制部分獲得更深入的探討，新增了 HJB 方程式、可控性（controllability）及自由時域問題（free-horizon problems）等內容。其他新增內容包括演化型微分賽局（evolutionary differential games），以及更豐富的反問題範例。類神經網路一章也進一步擴充，介紹殘差網路（residual networks）與用於動力系統的儲備池計算（reservoir computing）。
作者簡介
Alfio Borzì, born 1965 in Catania (Italy), is the professor and chair of Scientific Computing at the Institute for Mathematics of the University of Würzburg, Germany. He studied Mathematics and Physics in Catania and Trieste where he received his PhD in Mathematics from Scuola Internazionale Superiore di Studi Avanzati (SISSA).
He served as Research Officer at the University of Oxford (UK) and as Assistant Professor at the University of Graz (Austria) where he completed his habilitation and was appointed as Associate Professor. Since 2011 he has been Professor of Scientific Computing at the University of Würzburg.
Alfio Borzi is the author of 4 mathematics books and numerous articles in journals. The main topics of his research and teaching activities are modelling and numerical analysis, numerical optimisation and machine learning, optimal control theory and scientific computing. He is member of the editorial board for SIAM Review and of the book series Advances in Mechanics and Mathematics (AMMA).
作者簡介(中文翻譯)
Alfio Borzì 於 1965 年出生於義大利卡塔尼亞，目前擔任德國維爾茨堡大學數學研究所科學計算講座教授及系主任。他在卡塔尼亞和的里雅斯特修習數學與物理，並於 Scuola Internazionale Superiore di Studi Avanzati (SISSA) 取得數學博士學位。
他曾任職於英國牛津大學，擔任研究主任；後於奧地利格拉茲大學擔任助理教授，期間完成教授資格論文（habilitation），並獲聘為副教授。自 2011 年起，他擔任維爾茨堡大學科學計算教授。
Alfio Borzi 著有 4 本數學書籍，並在多種學術期刊發表大量論文。他的研究與教學活動主要涵蓋建模與數值分析、數值最佳化與機器學習、最佳控制理論，以及科學計算。他是 SIAM Review 編輯委員會，以及 Advances in Mechanics and Mathematics (AMMA) 書系的成員。
