[Book]Principles of Mathematical Modeling Second Edition.pdf

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1、PrefaceMyGoalsForThisBookScienceandengineeringstudentsdependheavilyonconceptsofmath-ematicalmodeling.Inanagewherealmosteverythingisdoneonacomputer,itismyconvictionthatstudentsofengineeringandsciencearebetterservediftheyunderstandand“own”theunderlyingmathematicsthatthecomputersaredoingontheirbe

2、half.Mathematicsisanecessarylanguagefordoingengineeringandscience.Thiswillremaintruenomat-terhowgoodcomputationbecomes.Irepeatedlytellstudentsthatitisriskytoacceptcomputercalculationswithouthavingdonesomeparallelclosed-formmodelingtobenchmarkthecomputerresults.Withoutsuchbenchmarkingandvalidat

3、ion,howdoweknowthatthecomputerisn’ttalkingnonsense?Finally,Ifinditsatisfyingandfuntodomathematicalmanipula-tionsthatexplainhoworwhysomethinghappens,andtousemathematicstoobtaincorrespondingnumericaldataorpredictions.Thus,asitwasforthefirstedition,myprimarygoalforthissecondeditionremainstoengageth

4、ereaderindevelopingafoundationformathematicalmodeling.Further,knowingthatmathematicalmodelsarebuiltinarangeofdisciplinesincludingphysics,biology,ecology,economics,sociology,militarystrategy,aswellasallofthemanybranchesofengineeringandknowingthatmathematicalmodelingiscomprisedofaverydiverseseto

5、fskillsandtools,Ifocusedontechniquesofparticularinteresttoengineers,scientists,andotherswhomodelcontinuoussystems.xiiixivPrefaceFeaturesofThisEditionAidedbyavarietyofreviewerscommentsandsuggestions,thissecondeditionfeatures:•Amoreformalstatementofaprincipledapproachtomathematicalmodeling(inCha

6、pter1).Tenprinciplesarearticulatedandinvokedasapplicationsaredeveloped,andeachofthemisidentifiedbyakeyword(seebelow).•Some360problems,manyofwhicharedesignedtoreinforceskillsinmathematicalmanipulation.Manycouldbedonewithacomputeralgebrasystem(CAS),andthereareothersforwhichnumericalpro-gramscould

7、beused.However,givenmygoalsforthisbook,Iwouldaskstudentsdotheproblemsintheold-fashionedway.•Areorderingandexpansionoftheapplicationschaptersthatreflectssomesenseofincreasingcomplexity.•Expandedfigurecaptionsthatareintendedtobemoreinformat