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1、FirstEdition,2009ISBN9789380168333©Allrightsreserved.Publishedby:GlobalMedia1819,BhagirathPalace,ChandniChowk,Delhi-110006Email:globalmedia@dkpd.comTableofContents1.Somemathematicalproblemsandtheirsolution2.Nbodyproblemandmatterdescription3.Relativity4.Electromagnetism5.Quantum
2、mechanics6.Nbodyprobleminquantum7.Statisticalphysics8.Nbodyproblemsandstatisticalequilibrium9.Continuousapproximation10.Energyincontinuousmedia11.AppendixBoundary,spectralandevolutionproblemsAquickclassificationofvariousmathematicalproblemsencounteredinthemodelizationofphysical
3、phenomenaisproposedinthepresentchapter.Moreprecisely,theproblemsconsideredinthischapterarethosethatcanbereducedtothefindingofthesolutionofapartialdifferentialequation(PDE).Indeed,formanyphysicists,toprovideamodelofaphenomenonmeanstoprovideaPDEdescribingthisphenomenon.Theycanbeb
4、oundaryproblems,spectralproblems,evolutionproblems.GeneralideasaboutthemethodsofexactandapproximatesolvingofthosePDEisalsoproposedfootnote{Thereaderissupposedtohaveagoodknowledgeofthesolvingofordinarydifferentialequations.Agoodreferenceonthissubjectis).}.Thischaptercontainsnum
5、erousreferencestothe"physical"partofthisbookwhichjustifytheinterestgiventothosemathematicalproblems.InclassicalbooksaboutPDE,equationsareusuallyclassifiedintothreecategories:hyperbolic,parabolicandellipticequation.Thisclassificationisconnectedtotheproofofexistenceandunicityofth
6、esolutionsratherthantotheactualwayofobtainingthesolution.Wepresenthereanotherclassificationconnectedtothewayoneobtainsthesolutions:wedistinguishmainlyboundaryproblemsandevolutionproblems.Letusintroduceboundaryproblems:Problem:(Boundaryproblem)Findusuchthat:1.1.usatisfiestheboun
7、daryconditions.Thisclassofproblemscanbesolvedbyintegralmethodssectionchapmethint)andbyvariationalmethodssectionchapmetvar).Letusintroduceasecondclassofproblems:evolutionproblems.Initialconditionsareusuallyimpliedbytimevariables.Oneknowsattimet0thefunctionu(x,y,t0)andtrytogetthe
8、valuesofu(x,y,t)fortgreaterthant0.Thisoursecondclassof
