商品描述
This textbook offers an introduction to the mathematical modeling of complex living systems. The authors guide undergraduate students in modeling ecological and biomedical problems using differential equations, dynamical systems, and data-driven methods. The modeling process--including assumption formulation, model construction, numerical simulation, sensitivity analysis, prediction, and biological interpretation--is presented step by step. Through hands-on projects and case studies, students learn to apply mathematical techniques and numerical simulations to study glucose-insulin regulation in diabetes, tumor-immune interactions in cancer therapy, and multi-species dynamics in Chesapeake Bay ecosystem. Together, these projects link mathematical theory to meaningful practice, helping students develop technical skills while fostering an appreciation of mathematics as a powerful tool for discovery and decision-making. Accompanied by student exercises and supported by MATLAB(R) code, the book also provides instruction on fitting models to real data and performing parameter sensitivity analysis. The book is well-suited for upper-undergraduate coursework or independent study and serves as a valuable resource for those aspiring to be researchers and practitioners in the life sciences.
商品描述(中文翻譯)
這本教科書介紹了複雜生物系統的數學建模。作者指導大學本科生使用微分方程、動態系統和數據驅動方法來建模生態和生物醫學問題。建模過程——包括假設的形成、模型的構建、數值模擬、敏感性分析、預測和生物學解釋——逐步呈現。通過實作專案和案例研究，學生學會應用數學技術和數值模擬來研究糖尿病中的葡萄糖-胰島素調節、癌症治療中的腫瘤-免疫相互作用，以及切薩皮克灣生態系統中的多物種動態。這些專案將數學理論與有意義的實踐聯繫起來，幫助學生發展技術技能，同時培養對數學作為發現和決策強大工具的欣賞。書中附有學生練習，並支持 MATLAB(R) 代碼，還提供了將模型擬合到實際數據和執行參數敏感性分析的指導。這本書非常適合高年級本科課程或獨立學習，並且對於那些渴望成為生命科學研究者和實踐者的人來說，是一個寶貴的資源。
作者簡介
Iordanka Panayotova, Ph.D., is an Associate Professor of Mathematics at Christopher Newport University (CNU), where she has been teaching mathematical modeling for many years, integrating project-based and data-driven modeling into a wide range of undergraduate courses. She holds a Ph.D. in Applied Mathematics from the University of Wisconsin-Milwaukee (2005) and a Ph.D. in Computational Mathematics from the National Academy of Sciences of Belarus (2000). With a track record of over 30 peer-reviewed publications, Dr. Panayotova's recent work focuses on mathematical modeling for life sciences, including data-driven climate-ecosystem modeling that informs conservation and fisheries management decisions in Chesapeake Bay. Her mentoring and research activities have been supported in part by the NSF-CURM (Center for Undergraduate Research in Mathematics) program and the Innovation Hub at CNU. Having supervised numerous undergraduate research projects, she received the 2020 CNU Class of 2013 Alumni Mentorship Award and the 2023 CNU Faculty Award for Excellence in Interdisciplinarity. Dr. Panayotova currently serves as co-Editor-in-Chief of the CODEE Journal, an online peer-reviewed journal focused on the teaching and learning of differential equations. Maila Hallare, Ph.D., is an Associate Professor of Mathematics at the United States Air Force Academy. She received her doctorate in Mathematics from the University of Kansas and works in differential equations, dynamical systems, and mathematical modeling. Her teaching and research show how mathematical ideas help explain scientific, engineering, and military problems. She uses theoretical results to establish and understand the behavior of mathematical models. Dr. Hallare has supervised many undergraduate research projects in applied mathematics and enjoys mentoring new faculty in course design, publishing, and developing research projects. She served as Editor-in-Chief of the CODEE Journal from 2022 to 2025 and continues to support national efforts in differential equations education. She believes that mathematical modeling helps make ODEs and dynamical systems relevant and relatable in the classroom, and she values interdisciplinary collaboration with colleagues who share an interest in theoretical models. Viktoria Savatorova, Ph.D., is an Associate Professor in the Department of Mathematics at Central Connecticut State University where she teaches a range of math courses and integrates modeling projects into her curriculum. She received her Ph.D. in Applied Mathematics and Physics from Moscow Engineering Physics Institute (1996) and Doctor of Science (habilitation) degree from the Russian Ministry of Science and Education (2011). Her research interests encompass mathematical modeling for applications in engineering and life sciences, multiscale methods, differential equations, and dynamical systems. Dr.Savatorova has over 40 peer-reviewed publications, with recent work focusing on mathematical modeling for life sciences, including diabetes onset, blood glucose management, and data-informed modeling of climate change impacts on fish species in Long Island Sound. Her participation in the 2023-2024 MAA Preparation for Industrial Careers in Mathematics (PIC Math) Program has reinforced her commitment to interdisciplinary research and engaging students in real-world projects, aligning with her goal to enhance students' practical experience and preparation for mathematically intensive careers. Dr. Savatorova currently serves as co-Editor-in-Chief of the CODEE Journal.
作者簡介(中文翻譯)
Iordanka Panayotova 博士是克里斯多福·紐波特大學（Christopher Newport University, CNU）數學系的副教授，擁有多年教授數學建模的經驗，並將專案導向和數據驅動的建模整合到多種本科課程中。她於2005年獲得威斯康辛大學密爾沃基分校的應用數學博士學位，以及於2000年獲得白俄羅斯國家科學院的計算數學博士學位。Panayotova 博士擁有超過30篇經過同行評審的出版物，最近的研究工作專注於生命科學的數學建模，包括數據驅動的氣候-生態系統建模，這些研究為切薩皮克灣的保護和漁業管理決策提供了依據。她的指導和研究活動部分得到了 NSF-CURM（數學本科研究中心）計劃和 CNU 創新中心的支持。她指導了許多本科研究專案，並獲得了2020年 CNU 2013屆校友導師獎和2023年 CNU 跨學科卓越教學獎。Panayotova 博士目前擔任 CODEE Journal 的共同主編，這是一個專注於微分方程教學與學習的在線同行評審期刊。
Maila Hallare 博士是美國空軍學院的數學副教授。她在堪薩斯大學獲得數學博士學位，專注於微分方程、動態系統和數學建模。她的教學和研究展示了數學思想如何幫助解釋科學、工程和軍事問題。她利用理論結果來建立和理解數學模型的行為。Hallare 博士指導了許多應用數學的本科研究專案，並喜歡在課程設計、出版和研究專案開發方面指導新任教職員。她曾於2022年至2025年擔任 CODEE Journal 的主編，並持續支持全國在微分方程教育方面的努力。她相信數學建模有助於使常微分方程（ODEs）和動態系統在課堂上變得相關和易於理解，並重視與對理論模型有興趣的同事進行跨學科合作。
Viktoria Savatorova 博士是中央康乃狄克州立大學數學系的副教授，教授多種數學課程並將建模專案整合到課程中。她於1996年獲得莫斯科工程物理學院的應用數學和物理博士學位，並於2011年獲得俄羅斯科學與教育部的科學博士（habilitation）學位。她的研究興趣包括工程和生命科學應用的數學建模、多尺度方法、微分方程和動態系統。Savatorova 博士擁有超過40篇經過同行評審的出版物，最近的研究專注於生命科學的數學建模，包括糖尿病發作、血糖管理以及對長島聲魚類的氣候變化影響的數據驅動建模。她參加了2023-2024年 MAA 數學工業職業準備計劃（PIC Math），進一步強化了她對跨學科研究的承諾，並讓學生參與現實世界的專案，這與她提升學生實踐經驗和為數學密集型職業做準備的目標相符。Savatorova 博士目前擔任 CODEE Journal 的共同主編。
