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数学建模

数学建模

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作者: [美] 乔达诺著

出版社: 机械工业出版社

出版时间: 2003-05

版次: 1

ISBN: 9787111121541

定价: 59.00

装帧: 平装

开本: 16开

纸张: 胶版纸

页数: 538页

正文语种: 英语

丛书: 经典原版书库

分类: 自然科学

47人买过

　　数学建模这门课程在数学及其在各个领域的应用之间架起一座桥梁。本书介绍了速个建模过程的原理，通过本书的学习，学生将有机会在以下建模活动中亲身实践，增强解决问题的能力；设计创意模型和经验模型、模型分析以及模型研究。本书特点论证了离散动态系统、离散优化和仿真等技术如何促进现代应用数学的发展强调通过模型设计提高学生的创造性，展现模型构建的艺术特性，包括经验建模和仿真建模的思想将数学建模方法与多样化建模和置信度建立等更具创造性的方面结合起来在设计创意模型和经验模型、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随书光盘包含软件、附加的建模场景和项目以及过去数学建模竞赛的题目。 1modelingchange
introduction

example1：testingforproportionality
1.1modelingchangewithdifferenceequations
examplei：asavingscertificate
example2：mortgagingahome

1.2approximatingchangewithdifferenceequations
example1：growthofayeastculture
example2：growthofayeastculturerevisited
example3：spreadofacontagiousdisease
example4：decayofdigoxininthebloodstream
example5：heatingofacooledobject

1.3solutionstodynamicalsystems
example1：asavingscertificaterevisited
example2：sewagetreatment
example3：prescriptionfordigoxin
example4：aninvestmentannuity
example5：acheckingaccount
example6：aninvestmentannuityrevisited

1.4systemsofdifferenceequations
examplei：acarrentalcompany
example2：thebattleoftrafalgar
example3：competitivehuntermodel——spottedowlsandhawks
example4：votingtendenciesofthepoliticalparties

2themodelingprocess,proportionality,andgeometricsimilarityintroduction

2.1mathematicalmodels
example1：vehicularstoppingdistance
2.2modelingusingproportionality
example1：kepler'sthirdlaw
2.3modelingusinggeometricsimilarity
example1：raindropsfromamotionlesscloud
example2：modelingabassfishingderby
2.4automobilegasolinemileage
2.5bodyweightandheight,strengthandagility
modelfitting
introduction

3.1fittingmodelstodatagraphically
3.2analyticmethodsofmodelfitting
3.3applyingtheleast-squarescriterion
3.4choosingabestmodel
example1：vehicularstoppingdistance

4experimentalmodeling
introduction
4.1harvestinginthechesapeakebayandother
one-termmodels
example1：harvestingbluefish
example2：harvestingbluecrabs
4.2high-orderpolynomialmodels
example1：elapsedtimeofataperecorder
4.3smoothing：low-orderpolynomialmodels
example1：elapsedtimeofataperecorderrevisited
example2：elapsedtimeofataperecorderrevisitedagain
example3：vehiclestoppingdistance
example4：growthofayeastculture
4.4cubicsplinemodels
example1：vehiclestoppingdistancerevisited

5simulationmodeling
introduction
5.1simulatingdeterministicbehavior：areaunderacurve
5.2generatingrandomnumbers
5.3simulatingprobabilisticbehavior'
5.4inventorymodel：gasolineandconsumerdemand
5.5queuingmodels
example1：aharborsystem
example2：morningrushhour

6discreteprobabilisticmodeling
introduction
6.1probabilisticmodelingwithdiscretesystems
example1：rentalcarcompanyrevisited
example2：votingtendencies
6.2modelingcomponentandsystemreliability
example1：seriessystems
example2：parallelsystems
example3：seriesandparallelcombinations
6.3linearregression
example1：ponderosapines
example2：thebassfishingderbyrevisited

7discreteoptimizationmodeling
7.1anoverviewofdiscreteoptimizationmodeling
example1：determiningaproductionschedule
example2：spaceshuttlecargo
example3：approximationbyapiecewiselinearfunction
7.2linearprogramminghgeometricsolutions
example1：thecarpenter'sproblem
example2：adata-fittingproblem
7.3linearprogrammingihalgebraicsolutions
example1：solvingthecarpenter'sproblemalgebraically
7.4linearprogrammingiii：thesimplexmethod
example1：thecarpenter'sproblemrevisited
example2：usingthetableauformat
7.5linearprogrammingiv：sensitivityanalysis
7.6numericalsearchmethods
example1：usingthedichotomoussearchmethod
example2：usingthegoldensectionsearchmethod
example3：model-fittingcriterionrevisited
example4：optimizingindustrialflow

8dimensionalanalysisandsimilitude
introduction
8.1dimensionsasproducts
example1：asimplependulum
example2：windforceonavan
8.2theprocessofdimensionalanalysis
examplel：terminalvelocityofaraindrop
example2：automobilegasmileagerevisited
8.3adampedpendulum
8.4examplesillustratingdimensionalanalysis
examplei：explosionanalysis
example2：howlongshouldyouroastaturkey?
8.5similitude
examplei：dragforceonasubmarine

9graphsoffunctionsasmodels
9.1anarmsrace
example1：civildefense
example2：mobilelaunchingpads
example3：multiplewarheads
example4：mirvsrevisited：countingwarheads
9.2modelinganarmsraceinstages
9.3managingnonrenewableresources：theenergycrisis
9.4effectsoftaxationontheenergycrisis
9.5agasolineshortageandtaxation

10modelingwithadifferentialequation
introduction
10.1populationgrowth
10.2prescribingdrugdosage
10.3brakingdistancerevisited
10.4graphicalsolutionsofautonomousdifferentialequations
example1：drawingaphaselineandsketching
solutioncurves
example2：coolingsoup
example3：logisticgrowthrevisited
10.5numericalapproximationmethods
example1：usingeuler'smethod
example2：asavingscertificaterevisited

11modelingwithsystemsofdifferentialequations
introduction
11.1graphicalsolutionsofautonomoussystemsoffirst-order
differentialequations
example1：alinearautonomoussystem
example2：anonlinearautonomoussystem
11.2acompetitivehuntermodel
11.3apredator-preymodel
11.4twomilitaryexamples
examplei：lanchestercombatmodels
example2：economicaspectsofanarmsrace
11.5euler'smethodforsystemsofdifferentialequations
example1：usingeuler'smethodforsystems
example2：atrajectoryandsolutioncurves

12continuousoptimizationmodelingintroduction
12.1aninventoryproblem：minimizingthecostofdeliveryandstorage
12.2amanufacturingproblem：maximizingprofitinproducingcompetingproducts
12.3constrainedcontinuousoptimization
examplel：anoiltransfercompany
example2：aspaceshuttlewatercontainer
12.4managingrenewableresources：thefishingindustry
aproblemsfromthemathematicscontestinmodeling.1985-
banelevatorsimulationalgorithms
ctherevisedsimplexmethod
index
内容简介:
　　数学建模这门课程在数学及其在各个领域的应用之间架起一座桥梁。本书介绍了速个建模过程的原理，通过本书的学习，学生将有机会在以下建模活动中亲身实践，增强解决问题的能力；设计创意模型和经验模型、模型分析以及模型研究。本书特点论证了离散动态系统、离散优化和仿真等技术如何促进现代应用数学的发展强调通过模型设计提高学生的创造性，展现模型构建的艺术特性，包括经验建模和仿真建模的思想将数学建模方法与多样化建模和置信度建立等更具创造性的方面结合起来在设计创意模型和经验模型、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随书光盘包含软件、附加的建模场景和项目以及过去数学建模竞赛的题目。
目录:
1modelingchange
introduction

example1：testingforproportionality
1.1modelingchangewithdifferenceequations
examplei：asavingscertificate
example2：mortgagingahome

1.2approximatingchangewithdifferenceequations
example1：growthofayeastculture
example2：growthofayeastculturerevisited
example3：spreadofacontagiousdisease
example4：decayofdigoxininthebloodstream
example5：heatingofacooledobject

1.3solutionstodynamicalsystems
example1：asavingscertificaterevisited
example2：sewagetreatment
example3：prescriptionfordigoxin
example4：aninvestmentannuity
example5：acheckingaccount
example6：aninvestmentannuityrevisited

1.4systemsofdifferenceequations
examplei：acarrentalcompany
example2：thebattleoftrafalgar
example3：competitivehuntermodel——spottedowlsandhawks
example4：votingtendenciesofthepoliticalparties

2themodelingprocess,proportionality,andgeometricsimilarityintroduction

2.1mathematicalmodels
example1：vehicularstoppingdistance
2.2modelingusingproportionality
example1：kepler'sthirdlaw
2.3modelingusinggeometricsimilarity
example1：raindropsfromamotionlesscloud
example2：modelingabassfishingderby
2.4automobilegasolinemileage
2.5bodyweightandheight,strengthandagility
modelfitting
introduction

3.1fittingmodelstodatagraphically
3.2analyticmethodsofmodelfitting
3.3applyingtheleast-squarescriterion
3.4choosingabestmodel
example1：vehicularstoppingdistance

4experimentalmodeling
introduction
4.1harvestinginthechesapeakebayandother
one-termmodels
example1：harvestingbluefish
example2：harvestingbluecrabs
4.2high-orderpolynomialmodels
example1：elapsedtimeofataperecorder
4.3smoothing：low-orderpolynomialmodels
example1：elapsedtimeofataperecorderrevisited
example2：elapsedtimeofataperecorderrevisitedagain
example3：vehiclestoppingdistance
example4：growthofayeastculture
4.4cubicsplinemodels
example1：vehiclestoppingdistancerevisited

5simulationmodeling
introduction
5.1simulatingdeterministicbehavior：areaunderacurve
5.2generatingrandomnumbers
5.3simulatingprobabilisticbehavior'
5.4inventorymodel：gasolineandconsumerdemand
5.5queuingmodels
example1：aharborsystem
example2：morningrushhour

6discreteprobabilisticmodeling
introduction
6.1probabilisticmodelingwithdiscretesystems
example1：rentalcarcompanyrevisited
example2：votingtendencies
6.2modelingcomponentandsystemreliability
example1：seriessystems
example2：parallelsystems
example3：seriesandparallelcombinations
6.3linearregression
example1：ponderosapines
example2：thebassfishingderbyrevisited

7discreteoptimizationmodeling
7.1anoverviewofdiscreteoptimizationmodeling
example1：determiningaproductionschedule
example2：spaceshuttlecargo
example3：approximationbyapiecewiselinearfunction
7.2linearprogramminghgeometricsolutions
example1：thecarpenter'sproblem
example2：adata-fittingproblem
7.3linearprogrammingihalgebraicsolutions
example1：solvingthecarpenter'sproblemalgebraically
7.4linearprogrammingiii：thesimplexmethod
example1：thecarpenter'sproblemrevisited
example2：usingthetableauformat
7.5linearprogrammingiv：sensitivityanalysis
7.6numericalsearchmethods
example1：usingthedichotomoussearchmethod
example2：usingthegoldensectionsearchmethod
example3：model-fittingcriterionrevisited
example4：optimizingindustrialflow

8dimensionalanalysisandsimilitude
introduction
8.1dimensionsasproducts
example1：asimplependulum
example2：windforceonavan
8.2theprocessofdimensionalanalysis
examplel：terminalvelocityofaraindrop
example2：automobilegasmileagerevisited
8.3adampedpendulum
8.4examplesillustratingdimensionalanalysis
examplei：explosionanalysis
example2：howlongshouldyouroastaturkey?
8.5similitude
examplei：dragforceonasubmarine

9graphsoffunctionsasmodels
9.1anarmsrace
example1：civildefense
example2：mobilelaunchingpads
example3：multiplewarheads
example4：mirvsrevisited：countingwarheads
9.2modelinganarmsraceinstages
9.3managingnonrenewableresources：theenergycrisis
9.4effectsoftaxationontheenergycrisis
9.5agasolineshortageandtaxation

10modelingwithadifferentialequation
introduction
10.1populationgrowth
10.2prescribingdrugdosage
10.3brakingdistancerevisited
10.4graphicalsolutionsofautonomousdifferentialequations
example1：drawingaphaselineandsketching
solutioncurves
example2：coolingsoup
example3：logisticgrowthrevisited
10.5numericalapproximationmethods
example1：usingeuler'smethod
example2：asavingscertificaterevisited

11modelingwithsystemsofdifferentialequations
introduction
11.1graphicalsolutionsofautonomoussystemsoffirst-order
differentialequations
example1：alinearautonomoussystem
example2：anonlinearautonomoussystem
11.2acompetitivehuntermodel
11.3apredator-preymodel
11.4twomilitaryexamples
examplei：lanchestercombatmodels
example2：economicaspectsofanarmsrace
11.5euler'smethodforsystemsofdifferentialequations
example1：usingeuler'smethodforsystems
example2：atrajectoryandsolutioncurves

12continuousoptimizationmodelingintroduction
12.1aninventoryproblem：minimizingthecostofdeliveryandstorage
12.2amanufacturingproblem：maximizingprofitinproducingcompetingproducts
12.3constrainedcontinuousoptimization
examplel：anoiltransfercompany
example2：aspaceshuttlewatercontainer
12.4managingrenewableresources：thefishingindustry
aproblemsfromthemathematicscontestinmodeling.1985-
banelevatorsimulationalgorithms
ctherevisedsimplexmethod
index

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