COMPUTATIONAL PARTIAL DIFFERENTIAL EQUATIONS FOR ENGINEERING SCIENCES -- COMPUTATIONAL PARTIAL DIFFERENTIAL EQUATIONS FOR ENGINEERING SCIENCES -- Contents -- Preface -- Heat Conduction and Diffusion -- 1.1.Fourier'sLaw -- 1.2.Energy -- 1.3.HeatEquation -- 1.3.1.Initial-BoundaryConditions -- 1.3.2.One-DimensionalEquation -- 1.3.3.HeatConductioninMovingMedia -- 1.4.Fick'sLawandDiffusion -- 1.4.1.DiffusioninMovingMedia -- 1.5.PorousMediaandDarcy'sLaw -- 1.5.1.SaturatedFluids -- 1.6.Phase-ChangeProblems -- 1.7.MatlabInterlude1 -- 1.7.1.CreatingMatrices -- 1.7.2.Sub-matrices -- 1.7.3.MatrixManipulations -- 1.7.4.TridiagonalMatrices -- 1.7.5.AlgebraicOperations -- 1.7.6.LeftandRightDivision -- 1.7.7.FlowControlStructure:ForLoop -- 1.7.8.ScriptFiles -- Finite-Difference Method -- 2.1.FiniteDifferences -- 2.1.1.ApproximationofDerivatives -- 2.1.2.CentralApproximation -- 2.1.3.Three-PointApproximations -- 2.1.4.FunctionsinTwoVariables -- 2.1.5.Higher-OrderDerivatives -- 2.1.6.ApproximationstoMixedDerivatives -- 2.2.ForwardEulerMethod -- 2.2.1.DirichletProblem -- 2.3.IntroductiontoStability -- 2.4.Consistency -- 2.5.Convergence -- 2.6.BoundaryValueProblems -- 2.6.1.NeumannProblem -- 2.6.2.RobinProblem -- 2.6.3.HeatConductioninMulti-layerBodies -- 2.7.BackwardEulerMethod -- 2.7.1.NeumannandRobinProblems -- 2.7.2.ConsistencyoftheBackwardEulerMethod -- 2.7.3.Non-dimensionalHeatEquation -- 2.8.Steady-StateDiffusion -- 2.8.1.Dirichlet-RobinProblem -- 2.8.2.NeumannProblem -- 2.9.MatlabInterlude2 -- 2.9.1.FunctionFiles -- 2.9.2.Central,ForwardandBackwardFunctions -- 2.9.3.FunctionwithMultipleOutputVariable -- 2.9.4.FlowControlStructures -- 2.9.5.Subfunctions -- 2.9.6.UsefulCommandsforFunctions.AnonymousFunctions -- 2.9.7.LogicalOperatorsandLogicalFunctions -- 2.9.8.EulerFunctions -- 2.9.9.FunctionsforSteady-StateProblems -- Parabolic Equations.

3.1.Crank-NicolsonMethod -- 3.1.1.DirichletProblem -- 3.1.2.RobinProblemfortheCrank-NicolsonMethod -- 3.2.VonNeumannStability -- 3.2.1.VonNeumannCriterion.Examples -- 3.2.2.CombinedMethod -- 3.3.DuFort-FrankelMethod -- 3.3.1.RichardsonMethod -- 3.3.2.DuFort-FrankelMethod -- 3.3.3.Stability -- 3.3.4.AnalysisofConsistency -- 3.3.5.MatrixformofDuFort-FrankelMethod -- 3.4.MatrixStability -- 3.5.Convection-DiffusionEquation -- 3.5.1.ExplicitMethods -- 3.5.2.BackwardEulerMethod -- 3.5.3.Crank-NicolsonImplicitMethod -- 3.5.4.DiffusionwithDecay -- 3.6.MethodofLines -- 3.6.1.DirichletProblem -- 3.6.2.NeumannProblem -- 3.6.3.Convection-DiffusionEquation -- 3.7.VariableCoeffcients -- 3.8.NonlinearEquations -- 3.8.1.ExplicitMethod -- 3.8.2.MethodofLines -- 3.9.MatlabInterlude3 -- 3.9.1.CrankFunction -- 3.9.2.RichardsonFunction -- 3.9.3.Dufort1Function -- 3.9.4.UpwindFunction -- 3.9.5.Convection1Function -- 3.9.6.MolFunctions -- 3.9.7.BurgersFunction -- 3.9.8.NonlinearFunction -- Finite Element Method -- 4.1.EssentialNumericalIntegration -- 4.1.1.RectangleRule -- 4.1.2.TrapeziumRule -- 4.1.3.Simpson'sRule -- 4.1.4.MultipleIntegrals -- 4.2.AxialMotionsofBars -- 4.2.1.ConcentratedForces -- 4.2.2.Statics -- 4.3.FEMforOrdinaryDifferentialEquations -- 4.3.1.WeakForm -- 4.3.2.MethodofWeightedResiduals -- 4.3.3.FiniteElementMethod.GalerkinMethod -- 4.3.4.Hat-ShapedFunctions -- 4.3.5.DirichletProblem -- 4.3.6.Dirichlet-NeumannProblem -- 4.3.7.ProblemsinStaticsofBars -- 4.3.8.PureNeumannProblem -- 4.3.9.Steady-StateThermalProcessinMultilayeredBody -- 4.4.DiracDeltaFunction -- 4.4.1.DiracFunctionandConcentratedForces -- 4.4.2.BouncingBall -- 4.4.3.HeavisideFunction -- 4.5.Time-DependentProblems -- 4.5.1.HeatEquation.DirichletProblem -- 4.5.2.NeumannProblem -- 4.5.3.WaveEquation -- 4.5.4.DirichletProblem -- 4.5.5.NeumannProblem -- 4.6.MatlabInterlude4.

4.6.1.SimpsonFunction -- 4.6.2.Simpson2dFunction -- 4.6.3.OdeFunctions -- 4.6.4.BarFunctions -- 4.6.5.LayersfemFunction -- 4.6.6.BallFunction -- 4.6.7.HeatFunctions -- 4.6.8.WaveFunctions -- Wave Motions -- 5.1.One-DimensionalContinuum -- 5.1.1.LocalEquations.ConcentratedForces -- 5.1.2.Strings -- 5.2.WaveEquation -- 5.2.1.Visco-elasticModels -- 5.2.2.TelegraphEquation -- 5.3.Courant-Friederichs-LewyMethod -- 5.3.1.DirichletProblem -- 5.3.2.MatrixForm -- 5.3.3.ConcentratedForces -- 5.3.4.NeumannandRobinProblems -- 5.3.5.ConsistencyofCFLMethod -- 5.3.6.ElasticForce -- 5.3.7.DampedWaveEquation -- 5.3.8.RefectionofWavesatDiscontinuities -- 5.4.Crank-NicolsonImplicitMethod -- 5.4.1.Initial-BoundaryProblems -- 5.4.2.ConsistencyofCrank-NicolsonMethod -- 5.4.3.StringonVisco-elasticBase -- 5.4.4.WeightedImplicitMethod -- 5.5.MethodofLinesfortheWaveEquation -- 5.5.1.ANonlinearWaveEquation -- 5.6.First-OrderEquations -- 5.6.1.Initial-Boundary-ValueProblem -- 5.6.2.VariableCoeffcient -- 5.6.3.ImplicitMethods -- 5.6.4.TheEquationUt+aUx=cU -- 5.6.5.Lax-FriederichsMethod -- 5.6.6.Lax-WendroffMethod -- 5.6.7.Three-Time-LevelMethod -- 5.6.8.McCormackMethod -- 5.7.NonlinearEquations.ConservativeForm -- 5.7.1.EquationforTraffcFlow -- 5.7.2.FiniteDifferenceMethodsforNonlinearEquations -- 5.8.SystemsofFirst-OrderEquations -- 5.8.1.HyperbolicModelofHeatConduction -- 5.8.2.Lax-WendroffMethodforSystems -- 5.8.3.McCormackMethodforSystems -- 5.8.4.NonlinearSystems -- 5.9.MatlabInterlude5 -- 5.9.1.CfFunctions -- 5.9.2.NicolsonFunction -- 5.9.3.MolwaveFunctions -- 5.9.4.UpwindMethods -- 5.9.5.AdvectionFunction -- 5.9.6.WendroffFunction -- 5.9.7.ConservativeFunctions -- 5.9.8.MacFunction -- Elliptic Equations -- 6.1.HistoricalModel -- 6.2.Finite-DifferenceMethod -- 6.2.1.Five-PointMethod -- 6.2.2.TruncationError -- 6.2.3.PoissonEquation -- 6.2.4.CurvedBoundary.

6.2.5.Seven-PointMethod -- 6.3.Green'sIdentities.UniquenessofSolutions -- 6.3.1.DirichletProblem -- 6.3.2.NeumannProblem.MixedProblem -- 6.3.3.RobinProblem -- 6.4.NeumannProblem:FivePointMethod -- 6.4.1.CurvedBoundary -- 6.5.FEMinTwoSpaceDimensions -- 6.5.1.BasisFunctions -- 6.5.2.DirichletProblem.WeakForm -- 6.5.3.Dirichlet-NeumannProblem -- 6.6.MatlabInterlude6 -- 6.6.1.FivepointFunction -- 6.6.2.CurvedFunction -- 6.6.3.Dam1Function -- 6.6.4.PyramidFunction -- 6.6.5.LaplaceFunction -- 6.6.6.NeumannFunction -- 6.6.7.PilewallFunction -- 6.6.8.Dam2Function -- Beam Equation -- 7.1.Euler-BernoulliBeamEquation -- 7.1.1.Initial-BoundaryConditions -- 7.2.Finite-DifferenceMethods -- 7.2.1.MatrixForm -- 7.2.2.MethodofLinesfortheBeamEquation -- 7.2.3.DynamicResponseunderaPulsingAction -- 7.2.4.ProblemsinStatics -- 7.3.SolutionstoBeamEquation -- 7.4.FiniteElementMethods -- 7.4.1.ShapeFunctions -- 7.4.2.StiffnessMatrix.MassMatrix -- 7.4.3.LumpedMassMatrix -- 7.5.FEMinStatics -- 7.6.ConcentratedForces -- 7.7.MixedBeamElement -- 7.8.MatlabInterlude7 -- 7.8.1.BeamFunctions -- 7.8.2.PulsingFunctions -- 7.8.3.FunctionsforStatics -- 7.8.4.FunctionsforFEM -- 7.8.5.MixedFunctions -- Diffusion in Two and Three Space Dimensions -- 8.1.HeatEquation -- 8.1.1.3DExplicitMethod -- 8.1.2.DirichletProblem -- 8.1.3.NeumannProblem -- 8.1.4.ImplicitMethods -- 8.1.5.Crank-NicolsonMethod -- 8.2.HeatEquationinCurvilinearCoordinates -- 8.2.1.PolarCoordinates -- 8.2.2.CylindricalCoordinates -- 8.2.3.SphericalCoordinates -- 8.2.4.CircularSymmetry -- 8.2.5.TheisSolution -- 8.3.FiniteElementMethod -- 8.3.1.Symmetry -- 8.4.2DDuFort-FrankelMethod -- 8.4.1.StabilityAnalysis -- 8.5.MethodofLines -- 8.5.1.3DMOL -- 8.6.Convection-DiffusionEquation -- 8.6.1.ExplicitMethods -- 8.6.2.ImplicitMethods -- 8.6.3.3DMethods -- 8.6.4.Convection-DiffusionEquationwithDecay -- 8.7.MatlabInterlude8.

8.7.1.Euler2DFunctions -- 8.7.2.TrenchFunction -- 8.7.3.CircularFunction -- 8.7.4.TheisFunction -- 8.7.5.SymmetryFunction -- 8.7.6.TheisfemFunction -- 8.7.7.Dufort2DFunction -- 8.7.8.Upwind2DFunction -- 8.7.9.Crank2DFunction -- Elements of Linear Algebra -- A.1.EigenvaluesandEigenvectors -- A.2.SpectralRadius -- A.3.BlockMatrix -- A.4.VectorNorms -- A.5.MatrixNorms -- A.6.SimilarityTransformation -- A.7.HermitianMatrices -- A.8.MatlabInterludeA -- A.8.1.GeneratingEigenvalues -- A.8.2.GeneratingEigenvectors -- A.8.3.CommandsforEigenvalues -- A.8.4.Norms -- Classif cation of PDEs -- B.1.Second-OrderPDEs -- B.1.1.EquationsofSecondOrderwithnIndependentVariables -- B.2.SystemsofFirst-OrderPDEs -- B.2.1.ClassifcationofSystems -- B.3.MatlabInterludeB -- B.3.1.SaveFunction -- B.3.2.LoadFunction.ImportWizard -- B.3.3.SavingGraphs.CopyingandPasting -- References -- Index.