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System Modeling - Caltech Computing

Asked Fermiwhetherhe wasnotimpressed by theagreementbetweenourcalculated numbersandhismeasured , \Howmanyarbitraryparametersdidyouusefory ourcalculations?"I thoughtforamomentaboutourcut-o procedures andsaid,\Four."Hesaid,\I remembermyfriendJohnnyvonNeumannused to say,withfourparametersI can tanelephant,andwith veI canmakehimwigglehistrunk."FreemanDysonon describingthepredictionsof hismodelformeson-protonscatteringto EnricoFermoin 1953[8].A modelis a preciserepresentationof a System 'sdynamicsusedto an-swer choosedependsonthequestionsthatwe wishto answer,andso theremay be multiplemod-elsfora singlephysicalsystem,withdi erent levelsof delity dependingonthephenomenaof thischapterwe providean introductionto theconceptof Modeling ,andprovidesomebasicmaterialontw o speci cmeth-odsthatarecommonlyusedin feedback andcontrolsystems:di erentialequationsanddi modelis a mathematicalrepresentationof a physical, ustoreasonabouta systemandmakepredictionsaboutwhoa systemwillbehave.

2.1. MODELING CONCEPTS 33 science for many centuries. One of the triumphs of Newton’s mechanics was the observation that the motion of the planets could be predicted based on the current positions and

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