Topics in Mathematical Modeling (Hardcover)

Topics in Mathematical Modeling is an introductory textbook on mathematical modeling. The book teaches how simple mathematics can help formulate and solve real problems of current research interest in a wide range of fields, including biology, ecology, computer science, geophysics, engineering, and the social sciences. Yet the prerequisites are minimal: calculus and elementary differential equations. Among the many topics addressed are HIV; plant phyllotaxis; global warming; the World Wide Web; plant and animal vascular networks; social networks; chaos and fractals; marriage and divorce; and El Niño. Traditional modeling topics such as predator-prey interaction, harvesting, and wars of attrition are also included. Most chapters begin with the history of a problem, follow with a demonstration of how it can be modeled using various mathematical tools, and close with a discussion of its remaining unsolved aspects.

Designed for a one-semester course, the book progresses from problems that can be solved with relatively simple mathematics to ones that require more sophisticated methods. The math techniques are taught as needed to solve the problem being addressed, and each chapter is designed to be largely independent to give teachers flexibility.

The book, which can be used as an overview and introduction to applied mathematics, is particularly suitable for sophomore, junior, and senior students in math, science, and engineering.

《數學建模專題》是一本介紹數學建模的入門教科書。本書教授如何利用簡單的數學方法來解決當前研究領域中的實際問題，涵蓋生物學、生態學、計算機科學、地球物理學、工程學和社會科學等多個領域。然而，先備知識要求很低，只需要有微積分和基礎微分方程的知識。本書涵蓋的主題包括HIV、植物葉序、全球變暖、互聯網、植物和動物的血管網絡、社交網絡、混沌和分形、婚姻和離婚以及厄爾尼諾現象。同時也包括了傳統的建模主題，如捕食者-獵物相互作用、收穫和消耗戰爭等。大多數章節以問題的歷史開始，然後演示如何使用各種數學工具進行建模，最後討論其尚未解決的方面。

本書設計為一學期課程，從可以用相對簡單的數學方法解決的問題開始，逐漸遞進到需要更複雜方法的問題。數學技巧是根據解決問題的需要進行教授，每個章節都設計為相對獨立，以給教師更大的靈活性。

本書可作為應用數學的概述和入門教材，特別適合數學、科學和工程專業的大二、大三和大四學生使用。