实用数学：建模分析逼近（影印版）

图书标准信息

• 作者 豪伊森 著
• 出版社 高等教育出版社
• 出版时间 2008-03
• 版次 1
• ISBN 9787040236071
• 定价 26.90元
• 装帧 平装
• 开本 16开
• 纸张 其他
• 页数 326页
• 正文语种 英语
• 丛书 天元基金影印数学丛书

【内容简介】

《实用数学：建模分析逼近（影印版）》内容分为三部分：建模，讲述了建模的一些原则（包括物理定律、本构关系及守恒定律），量纲分析（包括Buckingham的Pi定理）等;分析技巧，讲述了偏微分方程和广义函数的基础知识;渐近分析，讲述了渐近展开的基本概念，正则摄动展开，边界层和多重尺度法等。

【目录】

Preface
PartⅠModellingtechniques
1Thebasicsofmodelling
1.1Introduction
1.2Whatdowemeanbyamodel?
1.3Principlesofmodelling:physicallawsandconstitutiverelations
1.4Conservationlaws
1.5Generalremarks
1.6Exercises

2Units,dimensionsanddimensionalanalysis
2.1Introduction
2.2Unitsanddimensions
2.3Electricfieldsandelectrostatics
2.4Sourcesandfurtherreading
2.5Exercises

3Nondimensionalisation
3.1Nondimensionalisationanddimensionlessparameters
3.2TheNavier-StokesequationsandReynoldsnumbers
3.3BuckinghamsPi-theorem
3.4Sourcesandfurtherreading
3.5Exercises

4Casestudies:hairmodellingandcablelaying
4.1TheEuler-Bernoullimodelforabeam
4.2Hairmodelling
4.3Underseacablelaying
4.4Modellingandanalysis
4.5Sourcesandfurtherreading
4.6Exercise

5Casestudy:thethermistor(1)
5.1Heatandcurrentflowinthermistors
5.2Nondimensionalisation
5.3Athermistorinacircuit
5.4Sourcesandfurtherreading
5.5Exercises

6Casestudy:electrostaticpainting
6.1Electrostaticpainting
6.2Fieldequations
6.3Boundaryconditions
6.4Nondimensionalisation
6.5Sourcesandfurtherreading
6.6Exercises

PartⅡAnalyticaltechniques
7Partialdifferentialequations
7.1First-orderquasilinearpartialdifferentialequations:theory
7.2Example:Poissonprocesses
7.3Shocks
7.4Fullynonlinearequations:Charpitsmethod
7.5Second-orderlinearequationsintwovariables
7.6Furtherreading
7.7Exercises

8Casestudy:trafficmodelling
8.1Simplemodelsfortrafficflow
8.2Trafficjamsandotherdiscontinuoussolutions
8.3Moresophisticatedmodels
8.4Sourcesandfurtherreading
8.5Exercises

9Thedeltafunctionandotherdistributions
9.1Introduction
9.2Apointforceonastretchedstring;impulses
9.3InformaldefinitionofthedeltaandHeavisidefunctions
9.4Examples
9.5Balancingsingularities
9.6Greensfunctions
9.7Sourcesandfurtherreading
9.8Exercises

10Theoryofdistributions
10.1Testfunctions
10.2Theactionofatestfunction
10.3Definitionofadistribution
10.4Furtherpropertiesofdistributions
10.5Thederivativeofadistribution
10.6Extensionsofthetheoryofdistributions
10.7Sourcesandfurtherreading
10.8Exercises

11Casestudy:thepantograph
11.1Whatisapantograph?
11.2Themodel
11.3Impulsiveattachmentforanundampedpantograph
11.4Solutionnearasupport
11.5Solutionforawholespan
11.6Sourcesandfurtherreading
11.7Exercises

PartⅢAsymptotictechniques
12Asymptoticexpansions
12.1Introduction
12.2Ordernotation
12.3Convergenceanddivergence
12.4Furtherreading
12.5Exercises

13Regularperturbationexpansions
13.1Introduction
13.2Example:stabilityofaspacecraftinorbit
13.3Linearstability
13.4Example:thependulum
13.5Smallperturbationsofaboundary
13.6Caveatexpandator
13.7Exercises

14Casestudy:electrostaticpainting(2)
14.1Smallparametersintheelectropaintmodel
14.2Exercises

15Casestudy:pianotuning
15.1Thenotesofapiano:thetonalsystemofWesternmusic
15.2Tuninganidealpiano
15.3Arealpiano
15.4Sourcesandfurtherreading
15.5Exercises

16Boundarylayers
16.1Introduction
16.2Functionswithboundarylayers;matching
16.3Examplesfromordinarydifferentialequations
16.4Casestudy:cablelaying
16.5Examplesforpartialdifferentialequations
16.6Exercises

17Casestudy:thethermistor(2)
17.1Stronglytemperature-dependentconductivity
17.2Exercises

18Lubricationtheoryanalysisinlongthindomains
18.1Lubricationtheoryapproximations:slendergeometries
18.2Heatflowinabarofvariablecross-section
18.3Heatflowinalongthindomainwithcooling
18.4Advection-diffusioninalongthindomain
18.5Exercises

19Casestudy:continuouscastingofsteel
19.1Continuouscastingofsteel
19.2Exercises

20Lubricationtheoryforfluids
20.1Thinfluidlayers:classicallubricationtheory
20.2Thinviscousfluidsheetsonsolidsubstrates
20.3Thinfluidsheetsandfibres
20.4Furtherreading
20.5Exercises

21Casestudy:turningofeggsduringincubation
21.1Incubatingeggs
21.2Modelling
21.3Exercises

22Multiplescalesandothermethodsfornonlinearoscillators
22.1ThePoincare-Linstedtmethod
22.2Themethodofmultiplescales
22.3Relaxationoscillations
22.4Exercises

23RaytheoryandtheWKBmethod
23.1Introduction
23.2ClassicalWKBtheory
23.3Geometricopticsandraytheory:whydowesaylighttravelsinstraightlines?
23.4Kelvinsshipwaves
23.5Exercises
References
Index