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数学建模是用数学方法解决各种实际问题的桥梁。本书分离散建模和连续建模两部分介绍了整个建模过程的原理,通过本书的学习,学生将有机会在创造性模型和经验模型的构建、模型分析以及模型研究方面进行实践,增强解决问题的能力。
本书特点
论证了离散动力系统、离散优化等技术对现代应用数学发展的促进作用。
在创造性模型和经验模型的构建,模型分析以及模型研究中融入个人项目和小组项目,并且包含大量的例子和习题。
本版新增了关于图论建模的新的一章,从数学建模的角度介绍图论并鼓励学生对图论进行更深入的学习。
随书光盘中包含大学数学应用教学单元(UMAP),过去的建模竞赛试题,充满活力的跨学科应用研究课题,利用电子表格(Excel)、计算机代数系统(Maple、Mathematica、Matlab)以及图形计算器(TI)等技术的广泛的例子,在实验室环境下为学生设计的例子和习题。

1 Modeling Change
Introduction
1.1 Modeling Change with Difference Equations
1.2 Approximating Change with DifferenceEquations
1.3 Solutions to Dynamical Systems
1.4 Systems of Difference Equations
2 The Modeling Process, Proportionality,and Geometric Similarity
2.1 Mathematical Models
2.2 Modeling Using Proportionality
2.3 Modeling Using Geometric Similarity
2.4 Automobile Gasoline Mileage
2.5 Body Weight and Height, Strength and Agility
3 Model Fitting
3.1 Fitting Models to Data Graphically
3.2 Analytic Methods of Model Fitting
3.3 Applying the Least-Squares Criterion
3.4 Choosing a Best Model
4 Experimental Modeling
4.1 Harvesting in the Chesapeake Bay and Other One-Term Models
4.2 High-Order Polynomial Models
4.3 Smoothing: Low-Order Polynomial Models
4.4 Cubic Spline Models
5 Simulation Modeling
Introduction
5.1 Simulating Deterministic Behavior: Area Under a Curve
5.2 Generating Random Numbers
5.3 Simulating Probabilistic Behavior
5.4 Inventory Model: Gasoline and Consumer Demand
5.5 Queuing Models
6 Discrete Probabilistic Modeling
7 Optimization of Discrete Models
8 Modeling Using Graph Theory
9 Dimensional Analysis and Similitude
10 Graphs of Functions as Models
11 Modeling with a Differential Equation
12 Modeling with Systems of Differential Equations
13 Optimization of Continuous Models