Table Of Contentmore information - www.cambridge.org/9781107033856
Numerical Methods in Engineering with Python 3
Thisbookisanintroductiontonumericalmethodsforstudentsinengi-
neering.Itcoverstheusualtopicsfoundinanengineeringcourse:solu-
tionofequations,interpolationanddatafitting,solutionofdifferential
equations,eigenvalueproblems,andoptimization.Thealgorithmsare
implementedinPython3,ahigh-levelprogramminglanguagethatri-
valsMATLAB(cid:2)R inreadabilityandeaseofuse.Allmethodsincludepro-
grams showing how the computer code is utilized in the solution of
problems.
The book is based on Numerical Methods in Engineering with
Python, which used Python 2. Apart from the migration from Python
2toPython3,themajorchangeinthisnewtextistheintroductionof
thePythonplottingpackageMatplotlib.
Jaan Kiusalaas is a Professor Emeritus in the Department of Engi-
neering Science and Mechanics at Pennsylvania State University. He
has taught computer methods, including finite element and bound-
aryelementmethods,formorethan30years.Heisalsotheco-author
or author of four books – Engineering Mechanics: Statics; Engineering
Mechanics: Dynamics; Mechanics of Materials; Numerical Methods in
EngineeringwithMATLAB(2ndedition);andtwopreviouseditionsof
NumericalMethodsinEngineeringwithPython.
NUMERICAL
METHODS IN
ENGINEERING
WITH PYTHON 3
Jaan Kiusalaas
ThePennsylvaniaStateUniversity
cambridgeuniversitypress
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Firstpublished2013
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AcatalogrecordforthispublicationisavailablefromtheBritishLibrary.
LibraryofCongressCataloginginPublicationdata
Kiusalaas,Jaan.
NumericalmethodsinengineeringwithPython3/JaanKiusalaas.
pagescm
Includesbibliographicalreferencesandindex.
ISBN978-1-107-03385-6
1.Engineeringmathematics–Dataprocessing. 2.Python(Computerprogramlanguage) I.Title.
TA345.K58 2013
620.00285(cid:3)5133–dc23 2012036775
ISBN978-1-107-03385-6Hardback
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Contents
Preface....................................ix
1 IntroductiontoPython.......................................................1
1.1 GeneralInformation.............................................................1
1.2 CorePython.......................................................................4
1.3 FunctionsandModules.........................................................16
1.4 MathematicsModules..........................................................18
1.5 numpyModule..................................................................20
1.6 Plottingwithmatplotlib.pyplot........................................25
1.7 ScopingofVariables............................................................28
1.8 WritingandRunningPrograms...............................................29
2 SystemsofLinearAlgebraicEquations....................................31
2.1 Introduction.....................................................................31
2.2 GaussEliminationMethod.....................................................37
2.3 LUDecompositionMethods...................................................44
ProblemSet2.1........................................................................55
2.4 SymmetricandBandedCoefficientMatrices.................................59
2.5 Pivoting..........................................................................69
ProblemSet2.2........................................................................78
∗2.6 MatrixInversion.................................................................84
∗2.7 IterativeMethods...............................................................87
ProblemSet2.3........................................................................98
2.8 OtherMethods................................................................102
3 InterpolationandCurveFitting...........................................104
3.1 Introduction....................................................................104
3.2 PolynomialInterpolation.....................................................105
3.3 InterpolationwithCubicSpline..............................................120
ProblemSet3.1......................................................................126
3.4 Least-SquaresFit...............................................................129
ProblemSet3.2......................................................................141
4 RootsofEquations.........................................................145
4.1 Introduction....................................................................145
4.2 IncrementalSearchMethod..................................................146
v
vi Contents
4.3 MethodofBisection...........................................................148
4.4 MethodsBasedonLinearInterpolation.....................................151
4.5 Newton-RaphsonMethod....................................................156
4.6 SystemsofEquations..........................................................161
ProblemSet4.1......................................................................166
∗4.7 ZerosofPolynomials..........................................................173
ProblemSet4.2......................................................................180
4.8 OtherMethods................................................................182
5 NumericalDifferentiation.................................................183
5.1 Introduction....................................................................183
5.2 FiniteDifferenceApproximations............................................183
5.3 RichardsonExtrapolation.....................................................188
5.4 DerivativesbyInterpolation..................................................191
ProblemSet5.1......................................................................195
6 NumericalIntegration......................................................199
6.1 Introduction....................................................................199
6.2 Newton-CotesFormulas......................................................200
6.3 RombergIntegration..........................................................207
ProblemSet6.1......................................................................212
6.4 GaussianIntegration..........................................................216
ProblemSet6.2......................................................................230
∗6.5 MultipleIntegrals..............................................................232
ProblemSet6.3......................................................................243
7 InitialValueProblems......................................................246
7.1 Introduction....................................................................246
7.2 Euler’sMethod.................................................................247
7.3 Runge-KuttaMethods........................................................252
ProblemSet7.1......................................................................263
7.4 StabilityandStiffness.........................................................268
7.5 AdaptiveRunge-KuttaMethod..............................................271
7.6 Bulirsch-StoerMethod........................................................280
ProblemSet7.2......................................................................287
7.7 OtherMethods................................................................292
8 Two-PointBoundaryValueProblems.....................................293
8.1 Introduction....................................................................293
8.2 ShootingMethod..............................................................294
ProblemSet8.1......................................................................304
8.3 FiniteDifferenceMethod.....................................................307
ProblemSet8.2......................................................................317
9 SymmetricMatrixEigenvalueProblems.................................321
9.1 Introduction....................................................................321
9.2 JacobiMethod.................................................................324
9.3 PowerandInversePowerMethods..........................................336
ProblemSet9.1......................................................................345
9.4 HouseholderReductiontoTridiagonalForm...............................351
vii Contents
9.5 EigenvaluesofSymmetricTridiagonalMatrices............................359
ProblemSet9.2......................................................................368
9.6 OtherMethods................................................................373
10 IntroductiontoOptimization.............................................374
10.1 Introduction....................................................................374
10.2 MinimizationAlongaLine...................................................376
10.3 Powell’sMethod...............................................................382
10.4 DownhillSimplexMethod....................................................392
ProblemSet10.1.....................................................................399
Appendices..................................................................407
A1 TaylorSeries....................................................................407
A2 MatrixAlgebra.................................................................410
ListofProgramModules(byChapter).......417
Index....................................421
