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1、FourierSeriesandPartialDifferentialEquationsLectureNotesDrRuthE.BakerHilaryTerm2013ContentsPreface41Introduction61.1Initialandboundaryvalueproblems......................61.1.1Initial-valueproblem(IVP).......................61.1.2Boundary-valueproblem(BVP).....
2、...............61.1.3Existenceanduniqueness........................61.2Somepreliminaries................................71.3Theequationsweshallstudy..........................71.3.1Thewaveequation............................71.3.2Theheatequation................
3、............81.3.3Laplace’sequation............................82Fourierseries92.1Periodic,evenandoddfunctions........................102.1.1Propertiesofperiodicfunctions.....................112.1.2Oddandevenfunctions.........................112.2Fourierseries
4、forfunctionsofperiod2π....................122.2.1Question1................................122.2.2Sineandcosineseries..........................152.2.3Question2................................162.3ConvergenceofFourierseries..........................172.3.1Rateof
5、convergence...........................192.3.2GibbsPhenomenon............................192.4Functionsofanyperiod.............................192.4.1Sineandcosineseries..........................223Theheatequation253.1Derivationinonespacedimension..............
6、.........253.1.1Fourier’slaw...............................263.2Unitsandnondimensionalisation........................263.3Heatconductionina?niterod.........................273.4Initialandboundaryvalueproblem(IBVP)..................283.4.1ApplicationofFourierse
7、ries.......................293.5Uniqueness....................................303.6Non-zerosteadystate..............................312CONTENTS33.7Otherboundaryconditions...........................324Thewaveequation334.1Derivationinonespacedimension...........
8、............334.2Unitsandnondimensionalisation........................344.3Normalmodesofvibrationfora?nitestring.................354.4Initial-and-boundaryvalueproblemsfor?nitestrin
