A．FourImportantLinearPDEs
(1)Transportequation (2)Laplace equation
(3)Heatequation (4)Waveequation
B.NonlinearFirst-OrderPDE
(1)Completeintegrals,envelops (2)Characteristics
(3)Hamilton-Jacobiequation (4)Conservationlaws
C.OtherWaystoRepresentSolutions
(1)SeparationofVariables (2)SimilaritySolutions
(3)Transformmethods (4)ConvertingnonlinearintolinearPDE
(5)Asymptotics (6)PowerSeries
D.SobolevSpaces
(1)Holderspaces (2)Sobolevspaces (3)Approximation
(4)Extension (5)Traces (6)Sobolevinequalities
(7)Compactness (8)Additionaltopics (9)Otherspacesoffunctions