Mathematical Modelling with Case Studies: Using Maple and Matlab, Third Edition
暫譯: 案例研究的數學建模：使用 Maple 和 Matlab（第三版）
Barnes, B., Fulford, G. R.
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商品描述
Mathematical Modelling with Case Studies: Using Maple(TM) and MATLAB(R), Third Edition provides students with hands-on modelling skills for a wide variety of problems involving differential equations that describe rates of change. While the book focuses on growth and decay processes, interacting populations, and heating/cooling problems, the mathematical techniques presented can be applied to many other areas.
The text carefully details the process of constructing a model, including the conversion of a seemingly complex problem into a much simpler one. It uses flow diagrams and word equations to aid in the model-building process and to develop the mathematical equations. Employing theoretical, graphical, and computational tools, the authors analyze the behavior of the models under changing conditions. The authors often examine a model numerically before solving it analytically. They also discuss the validation of the models and suggest extensions to the models with an emphasis on recognizing the strengths and limitations of each model.
The highly recommended second edition was praised for its lucid writing style and numerous real-world examples. With updated Maple(TM) and MATLAB(R) code as well as new case studies and exercises, this third edition continues to give students a clear, practical understanding of the development and interpretation of mathematical models.
商品描述(中文翻譯)
《數學建模與案例研究：使用 Maple(TM) 和 MATLAB(R)，第三版》為學生提供了針對各種涉及描述變化率的微分方程問題的實作建模技能。雖然本書專注於增長與衰減過程、相互作用的族群以及加熱/冷卻問題，但所呈現的數學技術可以應用於許多其他領域。
本書詳細說明了構建模型的過程，包括將看似複雜的問題轉換為更簡單的問題。它使用流程圖和文字方程來輔助模型構建過程並發展數學方程。作者運用理論、圖形和計算工具，分析模型在變化條件下的行為。作者通常在進行解析解之前，先對模型進行數值分析。他們還討論了模型的驗證，並建議對模型進行擴展，強調認識每個模型的優勢和局限性。
備受推崇的第二版因其清晰的寫作風格和眾多的實際案例而受到讚譽。隨著更新的 Maple(TM) 和 MATLAB(R) 代碼以及新的案例研究和練習，這第三版繼續為學生提供對數學模型的發展和解釋的清晰、實用的理解。
作者簡介
B. Barnes is a director in the Australian Government Research Bureau and a visiting fellow at the National Centre for Epidemiology and Population Health at the Australian National University, Canberra. She has published work in a number of applied areas, such as bifurcation theory, population dynamics, carbon sequestration, biological processes, and disease transmission.
G.R. Fulford was recently a research associate and senior lecturer in applicable mathematics at the Queensland University of Technology. He has published several textbooks on mathematical modeling and industrial mathematics as well as other work in areas, such as mucus transport, spermatozoa propulsion, infectious disease modeling, tuberculosis in possums, tear-flow dynamics in the eye, and population genetics.
作者簡介(中文翻譯)
B. Barnes 是澳大利亞政府研究局的主任，也是澳大利亞國立大學堪培拉國家流行病學與人口健康中心的訪問研究員。她在多個應用領域發表了研究成果，包括分岔理論、人口動態、碳封存、生物過程和疾病傳播。
G.R. Fulford 最近擔任昆士蘭科技大學的研究助理和應用數學的高級講師。他出版了幾本有關數學建模和工業數學的教科書，以及在其他領域的研究，如黏液運輸、精子推進、傳染病建模、負鼠中的結核病、眼睛中的淚流動力學和人口遺傳學。
