偏微分方程讲义

图书标准信息

• 作者 [俄罗斯]阿诺德 著
• 出版社 世界图书出版公司
• 出版时间 2009-08
• 版次 1
• ISBN 9787510005046
• 定价 25.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 157页
• 正文语种 英语
• 原版书名 Lectures on Partial Differential Equations

【内容简介】

　　Inthemid-twentiethcenturythetheoryofpartialdifferentialequationswasconsideredthesummitofmathematics，bothbecauseofthedifficultyandsignificanceoftheproblemsitsolvedandbecauseitcameintoexistencelaterthanmostareasofmathematics.
　　Nowadaysmanyareinclinedtolookdisparaginglyatthisremarkableareaofmathematicsasanold-fashionedartofjugglinginequalitiesorasatestinggroundforapplicationsoffunctionalanalysis.Coursesinthissubjecthaveevendisappearedfromtheobligatoryprogramofmanyuniversities（forex-ample，inParis）.Moreover，suchremarkabletextbooksastheclassicalthree-volumeworkofGoursathavebeenremovedassuperfluousfromthelibraryoftheUniversityofParis-7（andonlythroughmyowninterventionwasitpossi-bletosavethem，alongwiththelecturesofKlein，Picard，Hermite，Darboux，Jordan）

【目录】

PrefacetotheSecondRussianEdition
1.TheGeneralTheoryforOneFirst-OrderEquationLiterature

2.TheGeneralTheoryforOneFirst-OrderEquation(Continued)Literature

3.HuygensPrincipleintheTheoryofWavePropagation.

4.TheVibratingString(dAlembertsMethod)
4.1.TheGeneralSolution
4.2.Boundary-ValueProblemsandtheCauchyProblem
4.3.TheCauehyProblemforanInfiniteStrifig.dAlembertsFormula
4.4.TheSemi-InfiniteString
4.5.TheFiniteString.Resonance
4.6.TheFourierMethod

5.TheFourierMethod(fortheVibratingString)
5.1.SolutionoftheProblemintheSpaceofTrigonometricPolynomials
5.2.ADigression
5.3.FormulasforSolvingtheProblemofSection5.1
5.4.TheGeneralCase
5.5.FourierSeries
5.6.ConvergenceofFourierSeries
5.7.GibbsPhenomenon

6.TheTheoryofOscillations.TheVariationalPrincipleLiterature

7.TheTheoryofOscillations.TheVariationalPrinciple(Continued)
8.PropertiesofHarmonicFunctions
8.1.ConsequencesoftheMean-ValueTheorem
8.2.TheMean-ValueTheoremintheMultidimensionalCase

9.TheFundamentalSolutionfortheLaplacian.Potentials
9.1.ExamplesandProperties
9.2.ADigression.ThePrincipleofSuperposition
9.3.Appendix.AnEstimateoftheSingle-LayerPotential

10.TheDouble-LayerPotential
10.1.PropertiesoftheDouble-LayerPotential

11SphericalFunctions.MaxwellsTheorem.TheRemovable
SingularitiesTheorem

12.Boundary-ValueProblemsforLaplaeesEquation.TheoryofLinearEquationsandSystems
12.1.FourBoundary-ValueProblemsforLaplacesEquation
12.2.ExistenceandUniquenessofSolutions
12.3.LinearPartialDifferentialEquationsandTheirSymbols

A.TheTopologicalContentofMaxwellsTheoremontheMultifieldRepresentationofSphericalFunctions
A.1.TheBasicSpacesandGroups
A.2.SomeTheoremsofRealAlgebraicGeometry
A.3.FromAlgebraicGeometrytoSphericalFunctions
A.4.ExplicitFormulas
A.5.MaxwellsTheoremandCp2/con≈S4
A.6.TheHistoryofMaxwellsTheorem
Literature

B.Problems
B.1.MaterialfrorntheSeminars
B.2.WrittenExaminationProblems.