偏微分方程（影印版）

　　This book is based on a course I have given five times at the University of Michigan， beginning in 1973. The aim is to present an introduction to a sampling of ideas， phenomena， and methods from the subject of partial differential equations that can be presented in one semester and requires no previous knowledge of differential equations. The problems， with hints and discussion， form an important and integral part of the course. In our department， students with a variety of specialties：notably differential geometry， numerical analysis， mathematical physics， complex analysis， physics， and partial differential equations：have a need for such a course.本书为英文版。

暂缺《偏微分方程（影印版）》作者简介

Preface
CHAPTERl
PowerSeriesMethods
1.1.TheSimplestPartialDifferentialEquation
1.2.ThelnitialValueProblemforOrdinaryDifferentialEquations
1.3.PowerSeriesandtheInitialValueProblemfor
PartialDifferentialEquations
1.4.TheFullyNonlinearCauchy-KowaleskayaTheorem
1.5.Cauchy-KowaleskayawithGeneralInitialSurfaces
1.6.TheSymboloraDifferentialOperator
1.7.Holmgren'sUniquenessTheorem
1.8.FritzJohn'sGlobalHolmgrenTheorem
1.9.CharacteristicsandSingularSolutions
CHAPTER2
SomeHarmonicAnalysis
2.1.TheSchwartzSpace(Rd)
2.2.TheFourierTransformon(Rd)
2.3.TheFourierTransformonLp(Rd):1≤p≤2
2.4.TemperedDistributions
2.5.Convolutionin(Rd)and(Rd)
2.6.L2DerivativesandSobolevSpaces
CHAPTER3
SolutionofInitialValueProblemsbyFourierSynthesis
3.1.Introduction
3.2.Schrodinger'sEquation
3.3.SolutionsofSchrodinger'sEquationwithDatain(Rd)
3.4.GeneralizedSolutionsofSchrodinger'sEquation
3.5.AlternateCharacterizationsoftheGeneralizedSolution
3.6.FourierSynthesisfortheHeatEquation
3.7.FourierSynthesisfortheWaveEquation
3.8.FourierSynthesisfortheCauchy-RiemannOperator
3.9.TheSidewaysHeatEquationandNullSolutions
3.10.TheHadamard-PetrowskyDichotomy
3.11.InhomogeneousEquations.Duhamel'sPrinciple
CHAPTER4
Propagatorsandx-SpaceMethods
4.1.Introduction
4.2.SolutionFormulasinxSpace
4.3.ApplicationsoftheHeatPropagator
4.4.ApplicationsoftheSchr6dingerPropagator
4.5.TheWaveEquationPropagatorford=1
4.6.Rotation-lnvariantSmoothSolutionsof
4.7.TheWaveEquationPropagatorford=3
4.8.TheMethodofDescent
4.9.RadiationProblems
CHAPIER5
TheDirichletProblem
5.1.Introduction
5.2.Dirichlet'sPrinciple
5.3.TheDirectMethodoftheCalculusofVariations
5.4.VariationsontheTheme
5.5.H1andtheDirichletBoundaryCondition
5.6.TheFredholmAlternative
5.7.EigenfunctionsandtheMethodofSeparationofVariables
5.8.TangentialRegularityfortheDirichletProblem
5.9.StandardEllipticRegularityTheorems
5.10.MaximumPrinciplesfromPotentialTheory
5.11.E.Hopf'sStrongMaximumPrinciples
APPENDIX
ACrashCourseinDistributionTheory
References
Index