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1、COMPUTATIONALPHYSICSMortenHjorth-JensenUniversityofOslo,Fall2009PrefaceSo,ultimately,inordertounderstandnatureitmaybenecessarytohaveadeeperunder-standingofmathematicalrelationships.Buttherealreasonisthatthesubjectisenjoyable,andalthoughwehumanscutnatureupindiffere
2、ntways,andwehavedifferentcoursesindifferentdepartments,suchcompartmentalizationisreallyartificial,andweshouldtakeourintellectualpleasureswherewefindthem.RichardFeynman,TheLawsofThermodynamics.Whyaprefaceyoumayask?Isn'tthatjustamereexpositionofaraisond'etreofanauthor
3、'schoiceofmaterial,preferences,biases,teachingphilosophyetc.?ToalargeextentIcananswerintheaffirmativetothat.Aprefaceoughttobepersonal.Indeed,whatyouwillseeinthevariouschaptersofthesenotesrepresentshowIperceivecomputationalphysicsshouldbetaught.Thissetoflecturenotes
4、servesthescopeofpresentingtoyouandtrainyouinanalgorithmicapproachtoproblemsinthesciences,representedherebytheunityofthreedisciplines,physics,mathematicsandinformatics.Thistrinityoutlinestheemergingfieldofcomputationalphysics.Ourinsightinaphysicalsystem,combinedwith
5、numericalmathematicsgivesustherulesforsettingupanalgorithm,viz.asetofrulesforsolvingaparticularproblem.Ourunderstandingofthephysicalsystemunderstudyisobviouslygaugedbythenaturallawsatplay,theinitialconditions,boundarycon-ditionsandotherexternalconstraintswhichinflu
6、encethegivensystem.Havingspelledoutthephysics,forexampleintheformofasetofcoupledpartialdifferentialequations,weneedefficientnumericalmethodsinordertosetupthefinalalgorithm.Thisalgorithmisinturncodedintoacomputerprogramandexecutedonavailablecomputingfacilities.Todeve
7、lopsuchanalgorithmicapproach,youwillbeexposedtoseveralphysicscases,spanningfromtheclassicalpendulumtoquantummechanicalsystems.Wewillalsopresentsomeofthemostpopularalgorithmsfromnumericalmathematicsusedtosolveaplethoraofproblemsinthesciences.Finallywewillcodifythes
8、ealgorithmsusingsomeofthemostwidelyusedprogramminglanguages,presentlyC,C++andFortrananditsmostrecentstandardFortran20031.However,ahigh-levelandfullyobje
