Mathematical Modeling 3e is a general introduction to an increasingly crucial topic for today's mathematicians. Unlike textbooks focused on one kind of mathematical model, this book covers the broad spectrum of modeling problems, from optimization to dynamical systems to stochastic processes. Mathematical modeling is the link between mathematics and the rest of the world. Meerschaert shows how to refine a question, phrasing it in precise mathematical terms. Then he encourages students to reverse the process, translating the mathematical solution back into a comprehensible, useful answer to the original question. This textbook mirrors the process professionals must follow in solving complex problems. Each chapter in this book is followed by a set of challenging exercises. These exercises require significant effort on the part of the student, as well as a certain amount of creativity. Meerschaert did not invent the problems in this book—they are real problems, not designed to illustrate the use of any particular mathematical technique. Meerschaert's emphasis on principles and general techniques offers students the mathematical background they need to model problems in a wide range of disciplines. This new edition will be accompanied by expanded and enhanced on-line support for instructors. MATLAB material will be added to complement existing support for Maple, Mathematica, and other software packages, and the solutions manual will be provided both in hard copy and on the web. • Increased support for instructors, including MATLAB material as well as other on-line resources
• New sections on time series analysis and diffusion models
• Additional problems with international focus such as whale and dolphin populations, plus updated optimization problems
Booknews The author introduces a five-step approach to mathematical modeling, which he demonstrates throughout the text. A variety of techniques and programs, such as Mathematica, MAPLE, and MINITAB, are used to solve a spectrum of realistic applications, from optimization to dynamical systems to stochastic processes. The book is divided into sections on each major type of mathematical model: optimization models, dynamic models, and probability models. Each chapter includes exercises. Annotation c. Book News, Inc., Portland, OR (booknews.com)

mathematical modeling and analysis (the original version 3)

Mathematical Modeling, Third Edition

数学建模方法与分析 = Mathematical modeling

數學建模方法與分析

(美)Mark M. Meerschaert著 ; 刘来福, 杨淳, 黄海洋译; 米尔斯切特; 刘来福; 杨淳; 黄海洋

Meerschaert, Mark

Academic Press, Incorporated

Elsevier (Singapore) Pte Ltd

Morgan Kaufmann Publishers

Elsevier Academic Press

China Machine Press

Brooks/Cole

機械工業出版社

3rd ed., Burlington, MA, Massachusetts, 2007

United States, United States of America

3. ed., [Nachdr, Amsterdam, 2008

China, People's Republic, China

3 edition, June 29, 2007

3rd ed, Amsterdam, ©2007

Singapore, Singapore

華章數學譯叢, 北京市, 2009

Bookmarks: p1 (p1): 第一部分 最优化模型
p1-1 (p1): 第1章 单变量最优化
p1-1-1 (p1): 1.1五步方法
p1-1-2 (p5): 1.2灵敏性分析
p1-1-3 (p9): 1.3灵敏性与稳健性
p1-1-4 (p11): 1.4习题
p1-1-5 (p13): 1.5进一步阅读文献
-1 (p14): 2.1无约束最优化
-1-1 (p23): 2.2拉格朗日乘子
-1-2 (p30): 2.3灵敏性分析与影子价格
-1-3 (p38): 2.4习题
-1-4 (p41): 2.5进一步阅读文献
-1 (p43): 3.1单变量最优化
-1-1 (p50): 3.2多变量最优化
-1-2 (p57): 3.3线性规划
-1-3 (p71): 3.4离散最优化
-1-4 (p81): 3.5习题
-1-5 (p88): 3.6进一步阅读文献
p2 (p89): 第二部分 动态模型
p2-1 (p89): 第4章 动态模型介绍
p2-1-1 (p89): 4.1定常态分析
p2-1-2 (p93): 4.2动力系统
p2-1-3 (p98): 4.3离散时间的动力系统
p2-1-4 (p103): 4.4习题
p2-1-5 (p106): 4.5进一步阅读文献
-1 (p108): 5.1特征值方法
-1-1 (p113): 5.2离散系统的特征值方法
-1-2 (p116): 5.3相图
-1-3 (p129): 5.4习题
-1-4 (p132): 5.5进一步阅读文献
-1 (p134): 6.1模拟简介
-1-1 (p139): 6.2连续时间模型
-1-2 (p145): 6.3欧拉方法
-1-3 (p150): 6.4混沌与分形
-1-4 (p161): 6.5习题
-1-5 (p171): 6.6进一步阅读文献
p3 (p173): 第三部分 概率模型
p3-1 (p173): 第7章 概率模型简介
p3-1-1 (p173): 7.1离散概率模型
p3-1-2 (p177): 7.2连续概率模型
p3-1-3 (p180): 7.3统计学简介
p3-1-4 (p183): 7.4扩散
p3-1-5 (p188): 7.5习题
p3-1-6 (p194): 7.6进一步阅读文献
-1 (p196): 8.1马尔可夫链
-1-1 (p204): 8.2马尔可夫过程
-1-2 (p212): 8.3线性回归
-1-3 (p219): 8.4时间序列
-1-4 (p228): 8.5习题
-1-5 (p234): 8.6进一步阅读文献
-1 (p236): 9.1蒙特卡罗模拟
-1-1 (p241): 9.2马尔可夫性质
-1-2 (p248): 9.3解析模拟
-1-3 (p254): 9.4习题
-1-4 (p257): 9.5进一步阅读文献
p4 (p259): 后记

本書系統介紹數學建模的理論及應用, 作者將數學建模的過程歸結為五個步驟 (即 "五步方法"), 並貫穿全書各類問題的分析和討論中. 本書闡述了如何使用數學模型來解決實際問題, 提出了在組建數學模型並且求解得到結論之後如何進行靈敏性和穩健性分析. 此外, 將數學建模方法與電腦的使用密切結合, 不僅通過對每個問題的討論給了很好的示範, 而且配備了大量的習題. 本書適合作為高等院校相關課程的教材和參考書, 也可供參加國內外數學建模競賽的人員參考. 本書提出了一種通用的數學建模方法 -- 五步方法, 幫助讀者迅速掌握數學建模的真諦. 作者以引人人勝的方式描述廠數學模型的3個主要領域 : 最優化.動力系統和隨機過程. 本書以實用的方法解決各式各樣的現實問題, 包括空間飛船的對接, 傳染病的增長率和野生生物的管理等. 此外, 本書根據需要詳細介紹了解決問題所需要的數學知識. 本版新增內容增加了關於時間序列分析和擴散模型的新節. 關注國際性問題, 如經濟預測, 人口控制, 蓄水池. 此外, 更新了最優化問題

We begin our discussion of optimization models at a place where most students will already have some practical experience.

本书阐述了如何使用数学模型来解决实际问题, 提出了在组建数学模型并且进行分析得到结论之后如何进行模型的灵敏性和稳健性分析

2023-12-04