ThisseventheditionofAdvancedEngineeringMathematicsdiffersfromthesixthinfourways.First,basedonreviewsandusercomments,newmaterialhasbeenadded,includingthefollowing.•Orthogonalprojectionsandleastsquaresapproximationsofvectorsandfunctions.Thisprovidesaunifyingthemeinrecognizingpartialsumsofeigenfunctionexpansionsasprojectionsontosubspaces,aswellasunderstandinglinesofbestfittodatapoints.•Orthogonalizationandtheproductionoforthogonalbases.•LUfactorizationofmatrices.•Lineartransformationsandmatrixrepresentations.•ApplicationoftheLaplacetransformtothesolutionofBessel’sequationandtoproblemsinvolvingwavemotionanddiffusion.•ExpandedtreatmentofpropertiesandapplicationsofLegendrepolynomialsandBesselfunctions,includingasolutionofKepler’sproblemandamodelofalternatingcurrentflow.•Heaviside’sformulaforthecomputationofinverseLaplacetransforms.•AcomplexintegralformulafortheinverseLaplacetransform,includinganapplicationtoheatdiffusioninaslab.•Vectoroperationsinorthogonalcurvilinearcoordinates.•ApplicationofvectorintegraltheoremstothedevelopmentofMaxwell’sequations.•AnapplicationoftheLaplacetransformconvolutiontoareplacementschedulingproblem.
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