| Foreword Table of Contents Notation 1 PartialDifferentialEquationsandTheirClassificationIntoTypes 1.1 Examples 1.2 ClassificationofSecond-OrderEquationsintoTypes 1.3 TypeClassificationforSystemsofFirstOrder 1.4 CharacteristicPropertiesoftheDifferentTypes 2 ThePotentialEquation 2.1 PosingtheProblem 2.2 SingularityFunction 2.3 TheMeanValuePropertyandMaximumPrinciple 2.4 ContinuousDependenceontheBoundaryData 3 ThePoissonEquation 3.1 PosingtheProblem 3.2 RepressentationoftheSolutionbytheGreenFunction 3.3 TheGreenFunctionfortheBall 3.4 TheNeumannBoundaryValueProblem 3.5 TheIntegralEquationMethod 4 DifferenceMethodsforthePoissonEquation 4.1 Introduction:TheOne-DimensionalCase 4.2 TheFive-PointFormula 4.3 M-matrices,MatrixNorms,PositiveDefiniteMatrices 4.4 PropertiesoftheMartrixLh 4.5&nb.. |
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