Lectures on Numerical Analysis

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1、LecturesonNumericalAnalysisDennisDeturckandHerbertS.WilfDepartmentofMathematicsUniversityofPennsylvaniaPhiladelphia,PA19104-6395Copyright2002,DennisDeturckandHerbertWilfApril30,20022Contents1DierentialandDierenceEquations51.1Introduction..........................

2、..........51.2Linearequationswithconstantcoecients...................81.3Dierenceequations...............................111.4Computingwithdierenceequations......................141.5Stabilitytheory..................................161.6Stabilitytheoryofdierenc

3、eequations.....................192TheNumericalSolutionofDierentialEquations232.1Euler'smethod..................................232.2Softwarenotes..................................262.3Systemsandequationsofhigherorder.....................292.4Howtodocumentaprogram.

4、.........................342.5Themidpointandtrapezoidalrules.......................382.6Comparisonofthemethods...........................432.7Predictor-correctormethods...........................482.8Truncationerrorandstepsize..........................502.9Controll

5、ingthestepsize.............................542.10Casestudy:Rockettothemoon........................602.11Mapleprogramsforthetrapezoidalrule....................652.11.1Example:Computingthecosinefunction...............672.11.2Example:Themoonrocketinonedimension.......

6、......682.12Thebigleagues..................................692.13LagrangeandAdamsformulas.........................744CONTENTS3Numericallinearalgebra813.1Vectorspacesandlinearmappings.......................813.2Linearsystems..................................863.3Bui

7、ldingblocksforthelinearequationsolver.................923.4Howbigiszero?.................................973.5Operationcount.................................1023.6Tounscrambletheeggs.............................1053.7Eigenvaluesandeigenvectorsofmatrices............

8、........1083.8TheorthogonalmatricesofJacobi.......................1123.9ConvergenceoftheJacobimethod.......................1153.10Corbato'sideaa