圣智学习

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。

Frank R．Giordano毕业于美国西点军校，曾任西点军校数学系系主任，现为美国海军研究生院教授，多年来一直是美国大学生数学建模竞赛的主要组织者，也是美国大学生数学建模竞赛组委会主任。

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
5．1 Simulating Deterministic Behavior: Area Under a Curve
5．2 6enerating Random Numbers
5．3 Simulating Probabilistic Behavior
5．4 Inventory Model: 6asoline and Consumer Demand
5．5 Queuing Models

6 Discrete Probabilistic Modeling
6．1 Probabilistic Modeling with Discrete Systems
6．2 Modeling Component and System Reliability
6．3 Linear Regression

7 Optimization of Discrete Models
7．1 An Overview of Optimization Modeling
7．2 Linear Programming I: Geometric Solutions
7．3 Linear Programming II: Algebraic Solutions
7．4 Linear Programming III: The Simplex Method
7．5 Linear Programming IV: Sensitivity Analysis

8 Modeling Using Graph Theory
8．1 Graphs as Models
8．2 Describing Graphs

9 Dimensional Analysis and Similitude
9．1 Dimensions as Products
9．2 The Process of Dimensional Analysis
9．3 A Damped Pendulum
9．4 Examples Illustrating Dimensional Analysis
9．5 Similitude

10 Graphs of Functions as Models
10．1 An Arms Race
10．2 Modeling an Arms Race in Stages
10．3 Managing Nonrenewable Resources: The Energy Crisis
10．4 Effects of Taxation on the Energy Crisis
10．5 A Gasoline Shortage and Taxation

11 Modeling with a Differential Equation
11．1 Population Growth
11．2 Prescribing Drug Dosage
11．3 Braking Distance Revisited
11．4 Graphical Solutions of Autonomous Differential Equations

12 Modeling with Systems of Differential Equations
12．1 Graphical Solutions of Autonomous Systems of First-Order Differential Equations
12．2 A Competitive Hunter Model
12．3 A Predator-Prey Model
12．4 Two Military Examples

13 Optimization of Continuous Models
13．1 An Inventory Problem: Minimizing the Cost of Delivery and Storage
13．2 A Manufacturing Problem: Maximizing Profit in Producing Competing Products
13．3 Constrained Continuous Optimization
13．4 Managing Renewable Resources: The Fishing Industry