文档介绍：WeijiuLiuDepartmentofMathematicsUniversityofCentralArkansasIntroductiontoPartialDifferentialEquationsDate1OverviewDate2WhatarePDEs?Anequationcontaininganunknownfunctionanditspartialderivatives::Heat(diffusion)equationdescribingheatconduction:Date4Convection-diffusionequationdescribingchemicaldiffusionandconvection:ConvectionDiffusoinDate5Hyperbolicequations:Waveequationdescribing thestringvibrationDate6Ellipticequations:Laplace’sequationDate7WhatwewanttodoabouttheequationsFindanexactsolutionFindanumericalsolutionStudytheirwell-posednessStudytheirstabilityDesignacontrollawtoforcetheirsolutiontoyourdesiredoneMore…Date8WhataremethodstofindasolutionSeparationofvariablesFourierseriesFouriertransformationLaplacetransformationMethodofcharacteristicsGreenfunctionsD’Alembert’sformulasSymmetryanalysisMore…Date9TentativescheduleDerivationoftheheatequation,1weekSeparationofvariablesforsolvingtheheatequationandLaplace’sequation,2weeksFourierseries,3weeksDerivationofthewaveequation,1weekSeparationofvariablesforsolvingthewaveequation,1weekHighdimensionalequations,3weeksNon-homogeneousproblems,2weeksEquationsoninfinitedomains,1weekDate10