数学建模 : 第4版

1ModelingChange

Introduction

1.1ModelingChangewithDifferenceEquations

1.2ApproximatingChangewithDifferenceEquations

1.3SolutionstoDynamicalSystems

1.4SystemsofDifferenceEquations

2TheModelingProcess,Proportionality,andGeometricSimilarity

2.1MathematicalModels

2.2ModelingUsingProportionality

2.3ModelingUsingGeometricSimilarity

2.4AutomobileGasolineMileage

2.5BodyWeightandHeight,StrengthandAgility

3ModelFitting

3.1FittingModelstoDataGraphically

3.2AnalyticMethodsofModelFitting

3.3ApplyingtheLeast-SquaresCriterion

3.4ChoosingaBestModel

4ExperimentalModeling

4.1HarvestingintheChesapeakeBayandOtherOne-TermModels

4.2High-OrderPolynomialModels

4.3Smoothing:Low-OrderPolynomialModels

4.4CubicSplineModels

5SimulationModeling

Introduction

5.1SimulatingDeterministicBehavior:AreaUnderaCurve

5.2GeneratingRandomNumbers

5.3SimulatingProbabilisticBehavior

5.4InventoryModel:GasolineandConsumerDemand

5.5QueuingModels

……

6DiscreteProbabilisticModeling

7OptimizationofDiscreteModels

8ModelingUsingGraphTheory

9DimensionalAnalysisandSimilitude

10GraphsofFunctionsasModels

11ModelingwithaDifferentialEquation

12ModelingwithSystemsofDifferentialEquations

13OptimizationofContinuousModels

　　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。