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ListofExercises
Exercise1.1:Compute1+1.................................
44
Exercise1.2:WriteaHelloWorldprogram ...................
44
Exercise1.3:Deriveandcomputeaformula...................
44
Exercise1.4:ConvertfrommeterstoBritishlengthunits.......
45
Exercise1.5:Computethemassofvarioussubstances..........
45
Exercise1.6:Computethegrowthofmoneyinabank..........
45
Exercise1.7:Finderror(s)inaprogram......................
45
Exercise1.8:Typeinprogramtext ..........................
45
Exercise1.9:Typeinprogramsanddebugthem...............
46
Exercise1.10:EvaluateaGaussianfunction ..................
47
Exercise1.11:Computetheairresistanceonafootball.........
47
Exercise1.12:Howtocooktheperfectegg....................
48
Exercise1.13:Derivethetrajectoryofaball..................
48
Exercise1.14:Finderrorsinthecodingofformulas............
49
Exercise1.15:Explainwhyaprogramdoesnotwork...........
50
Exercise1.16:FinderrorsinPythonstatements...............
50
Exercise1.17:Finderrorsinthecodingofaformula...........
50
Exercise2.1:MakeaFahrenheit-Celsiusconversiontable .......
84
Exercise2.2:GenerateanapproximateFahrenheit-Celsius
conversiontable..............................
84
Exercise2.3:Workwithalist...............................
84
Exercise2.4:Generateoddnumbers .........................
84
Exercise2.5:Sumofﬁrstnintegers..........................
85
Exercise2.6:Generateequallyspacedcoordinates .............
85
Exercise2.7:Makeatableofvaluesfromaformula............
85
Exercise2.8:Storevaluesfromaformulainlists...............
85
Exercise2.9:Simulateoperationsonlistsbyhand .............
86
Exercise2.10:Computeamathematicalsum..................
86
Exercise2.11:Replaceawhileloopbyaforloop ..............
86
Exercise2.12:Simulateaprogrambyhand...................
87
xxiii
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ListofExercises
Exercise2.13:ExplorePythondocumentation.................
87
Exercise2.14:Indexanestedlists ...........................
87
Exercise2.15:Storedatainlists.............................
88
Exercise2.16:Storedatainanestedlist .....................
88
Exercise2.17:Valuesofbooleanexpressions ..................
88
Exercise2.18:Exploreround-oﬀerrorsfromalargenumberof
inverseoperations ............................
89
Exercise2.19:Explorewhatzerocanbeonacomputer.........
89
Exercise2.20:Comparetworealnumberswithatolerance......
90
Exercise2.21:Interpretacode..............................
90
Exercise2.22:Exploreproblemswithinaccurateindentation ....
90
Exercise2.23:ExplorepunctuationinPythonprograms ........
91
Exercise2.24:Investigateaforloopoverachanginglist........
91
Exercise3.1:WriteaFahrenheit-Celsiusconversionfunction .... . 128
Exercise3.2:Evaluateasumandwriteatestfunction ......... . 128
Exercise3.3:Writeafunctionforsolvingax2+bx+c=0...... 129
Exercise3.4:Implementthesumfunction .................... . 129
Exercise3.5:Computeapolynomialviaaproduct............. 129
Exercise3.6:IntegrateafunctionbytheTrapezoidalrule....... 129
Exercise3.7:DerivethegeneralMidpointintegrationrule ...... . 131
Exercise3.9:Explainwhyaprogramworks................... 133
Exercise3.10:Simulateaprogrambyhand................... 134
Exercise3.11:Computetheareaofanarbitrarytriangle........ 134
Exercise3.12:Computethelengthofapath.................. 134
Exercise3.13:Approximateπ............................... 135
Exercise3.14:Writefunctions............................... 135
Exercise3.15:Approximateafunctionbyasumofsines........ 135
Exercise3.16:ImplementaGaussianfunction................. 136
Exercise3.17:Wrapaformulainafunction................... 136
Exercise3.18:Writeafunctionfornumericaldiﬀerentiation..... 137
Exercise3.19:Implementthefactorialfunction................ 137
Exercise3.20:Computevelocityandaccelerationfrom1Dposition
data........................................ 138
Exercise3.21:Findthemaxandminvaluesofafunction....... 138
Exercise3.22:Findthemaxandminelementsinalist......... 138
Exercise3.23:ImplementtheHeavisidefunction............... 139
Exercise3.24:ImplementasmoothedHeavisidefunction ....... . 139
Exercise3.25:Implementanindicatorfunction................ 139
Exercise3.26:Implementapiecewiseconstantfunction......... 140
Exercise3.27:Applyindicatorfunctions...................... 140
Exercise3.28:Testyourunderstandingofbranching ........... . 141
Exercise3.29:Simulatenestedloopsbyhand ................. . 141
Exercise3.30:Rewriteamathematicalfunction ............... . 142
Exercise3.31:Makeatableforapproximationsofcosx......... 142
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List ofExercises
xxv
Exercise3.32:UseNoneinkeywordarguments................ 143
Exercise3.33:Writeasortfunctionforalistof4-tuples........ 143
Exercise3.35:Findpairsofcharacters ....................... . 145
Exercise3.36:Countsubstrings ............................. . 145
Exercise3.37:Resolveaproblemwithafunction.............. 145
Exercise3.38:Determinethetypesofsomeobjects ............ . 146
Exercise3.39:Findanerrorinaprogram .................... . 146
Exercise4.1:Makeaninteractiveprogram.................... 211
Exercise4.5:Useexceptionstohandlewronginput ............ . 212
Exercise4.8:TryMSWordorLibreOﬃcetowriteaprogram.... 212
Exercise4.9:Prompttheuserforinputtoaformula........... 213
Exercise4.11:Useexceptionstohandlewronginput ........... . 213
Exercise4.12:Testvalidityofinputdata..................... 213
Exercise4.13:Raiseanexceptionincaseofwronginput........ 213
Exercise4.14:Evaluateaformulafordatainaﬁle............. 214
Exercise4.15:Computethedistanceittakestostopacar ...... . 214
Exercise4.16:Lookupcalendarfunctionality ................. . 215
Exercise4.17:UsetheStringFunctiontool.................... 215
Exercise4.18:Whywetestforspeciﬁcexceptiontypes ......... . 215
Exercise4.19:Makeacompletemodule ...................... . 215
Exercise4.20:Makeamodule............................... 216
Exercise4.22:Checkifmathematicalidentitieshold ........... . 216
Exercise4.23:Computeprobabilitieswiththebinomialdistribution 218
Exercise4.24:ComputeprobabilitieswiththePoissondistribution 219
Exercise5.1:Filllistswithfunctionvalues.................... 280
Exercise5.2:Fillarrays;loopversion ........................ . 280
Exercise5.3:Fillarrays;vectorizedversion ................... . 280
Exercise5.4:Plotafunction................................ 281
Exercise5.5:Applyafunctiontoavector .................... . 281
Exercise5.6:Simulatebyhandavectorizedexpression ......... . 281
Exercise5.7:Demonstratearrayslicing....................... 281
Exercise5.8:Replacelistoperationsbyarraycomputing........ 281
Exercise5.9:Plotaformula ................................ . 281
Exercise5.10:Plotaformulaforseveralparameters............ 282
Exercise5.11:Specifytheextentoftheaxesinaplot .......... . 282
Exercise5.12:PlotexactandinexactFahrenheit-Celsiusconversion
formulas .................................... . 282
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ListofExercises
Exercise5.13:Plotthetrajectoryofaball.................... 282
Exercise5.14:Plotdatainatwo-columnﬁle.................. 282
Exercise5.15:Writefunctiondatatoﬁle ..................... . 283
Exercise5.16:Plotdatafromaﬁle .......................... . 283
Exercise5.17:Fitapolynomialtodatapoints................. 284
Exercise5.18:Fitapolynomialtoexperimentaldata........... 285
Exercise5.21:Plotatrip’spathandvelocityfromGPScoordinates 286
Exercise5.22:VectorizetheMidpointruleforintegration....... 287
Exercise5.23:ImplementLagrange’sinterpolationformula...... 288
Exercise5.24:PlotLagrange’sinterpolatingpolynomial ........ . 289
Exercise5.25:InvestigatethebehaviorofLagrange’sinterpolating
polynomials ................................. . 289
Exercise5.26:Plotawavepacket............................ 290
Exercise5.27:Judgeaplot ................................. . 290
Exercise5.28:Plottheviscosityofwater ..................... . 290
Exercise5.29:Exploreacomplicatedfunctiongraphically....... 290
Exercise5.30:PlotTaylorpolynomialapproximationstosinx... 291
Exercise5.31:Animateawavepacket........................ 291
Exercise5.32:AnimateasmoothedHeavisidefunction ......... . 291
Exercise5.33:Animatetwo-scaletemperaturevariations........ 292
Exercise5.34:Usenon-uniformlydistributedcoordinatesfor
visualization................................. 292
Exercise5.35:Animateasequenceofapproximationstoπ ...... . 293
Exercise5.36:Animateaplanet’sorbit....................... 293
Exercise5.37:AnimatetheevolutionofTaylorpolynomials..... 294
Exercise5.38:Plotthevelocityproﬁleforpipeﬂow............. 295
Exercise5.39:Plotsum-of-sinesapproximationstoafunction ... . 295
Exercise 5.40: Animate the evolutionof a sum-of-sine
approximationtoafunction ................... . 295
Exercise5.41:Plotfunctionsfromthecommandline........... 296
Exercise5.42:Improvecommand-lineinput................... 296
Exercise5.43:Demonstrateenergyconceptsfromphysics....... 296
Exercise5.44:Plotaw-likefunction......................... 297
Exercise5.45:Plotapiecewiseconstantfunction .............. . 297
Exercise5.46:Vectorizeapiecewiseconstantfunction.......... 297
Exercise 5.47:Visualize approximationsin the Midpoint
integrationrule .............................. . 297
Exercise5.48:VisualizeapproximationsintheTrapezoidal
integrationrule .............................. . 298
Exercise5.49:Experienceoverﬂowinafunction............... 298
Exercise5.50:Applyafunctiontoarank2array.............. 299
Exercise5.51:Explainwhyarraycomputationsfail ............ . 299
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List ofExercises
xxvii
Exercise6.2:Exploresyntaxdiﬀerences:listsvs.dicts.......... 364
Exercise6.3:Usestringoperationstoimproveaprogram....... 364
Exercise6.4:Interpretoutputfromaprogram................. 364
Exercise6.6:Makeanesteddictionary ....................... . 365
Exercise6.7:Makeanesteddictionaryfromaﬁle.............. 365
Exercise6.8:Makeanesteddictionaryfromaﬁle.............. 365
Exercise6.9:Computetheareaofatriangle .................. . 366
Exercise6.10:Comparedatastructuresforpolynomials ........ . 366
Exercise6.11:Computethederivativeofapolynomial ......... . 366
Exercise6.12:Specifyfunctionsonthecommandline .......... . 367
Exercise6.13:Interpretfunctionspeciﬁcations ................ . 368
Exercise6.14:Compareaveragetemperaturesincities.......... 368
Exercise6.15:GenerateanHTMLreportwithﬁgures.......... 369
Exercise6.16:Allowdiﬀerenttypesforafunctionargument..... 369
Exercise6.17:Makeafunctionmorerobust................... 369
Exercise6.18:Findproportionofbasesinside/outsideexons .... . 370
Exercise7.1:Makeafunctionclass .......................... . 426
Exercise7.4:Makeclassesforarectangleandatriangle........ 427
Exercise7.6:Makeaclassforstraightlines................... 428
Exercise7.7:Flexiblehandlingoffunctionarguments .......... . 428
Exercise7.8:Wrapfunctionsinaclass ....................... . 428
Exercise7.9:Flexiblehandlingoffunctionarguments .......... . 429
Exercise7.10:Deduceaclassimplementation ................. . 429
Exercise7.11:Implementspecialmethodsinaclass............ 430
Exercise7.12:Makeaclassforsummationofseries ............ . 430
Exercise7.13:Applyanumericaldiﬀerentiationclass........... 431
Exercise7.14:Applysymbolicdiﬀerentiation.................. 431
Exercise7.15:Implementin-place+=and-=operators ......... . 431
Exercise7.16:Implementaclassfornumericaldiﬀerentiation.... 432
Exercise7.17:Examineaprogram........................... 433
Exercise7.18:Modifyaclassfornumericaldiﬀerentiation....... 433
Exercise7.19:MakeaclassfortheHeavisidefunction.......... 433
Exercise7.20:Makeaclassfortheindicatorfunction .......... . 434
Exercise7.21:Makeaclassforpiecewiseconstantfunctions..... 434
Exercise7.22:Speeduprepeatedintegralcalculations.......... 435
Exercise7.23:Applyaclassforpolynomials .................. . 435
Exercise7.24:Findabuginaclassforpolynomials............ 435
Exercise7.25:Implementsubtractionofpolynomials........... 436
Exercise7.26:Testthefunctionalityofprettyprintofpolynomials 436
Exercise7.27:Vectorizeaclassforpolynomials................ 436
ListofExercises
Exercise7.29:ExtendclassVec2Dtoworkwithlists/tuples..... 437
Exercise7.30:ExtendclassVec2Dto3Dvectors............... 438
Exercise7.31:UseNumPyarraysinclassVec2D .............. . 438
Exercise7.32:Makeclassesforstudentsandcourses ........... . 439
Exercise7.33:Findlocalandglobalextremaofafunction ...... . 439
Exercise7.34:Findtheoptimalproductionforacompany ...... . 440
Exercise8.1:Flipacointimes .............................. . 499
Exercise8.2:Computeaprobability ......................... . 500
Exercise8.3:Chooserandomcolors.......................... 500
Exercise8.4:Drawballsfromahat.......................... 500
Exercise8.5:Computingprobabilitiesofrollingdice ........... . 500
Exercise8.7:Computetheprobabilityofhandsofcards........ 501
Exercise8.10:Generalizeagame ............................ . 502
Exercise8.11:Comparetwoplayingstrategies................. 502
Exercise8.12:Investigatestrategiesinagame................. 502
Exercise8.13:Investigatethewinningchancesofsomegames ... . 502
Exercise8.14:Computeprobabilitiesofthrowingtwodice ...... . 503
Exercise8.15:Vectorizeﬂippingacoin....................... 503
Exercise8.16:Vectorizeaprobablilitycomputation............ 503
Exercise8.17:Throwdiceandcomputeasmallprobability ..... . 504
Exercise8.18:Diﬀerenceequationforrandomnumbers......... 504
Exercise8.19:Makeaclassfordrawingballsfromahat........ 504
Exercise8.20:Independentversusdependentrandomnumbers .. . 505
Exercise8.21:Computetheprobabilityofﬂippingacoin ....... . 505
Exercise8.22:Simulatebinomialexperiments ................. . 506
Exercise8.23:Simulateapokergame ........................ . 506
Exercise8.24:Estimategrowthinasimulationmodel.......... 506
Exercise8.25:Investigateguessingstrategies.................. 507
Exercise8.27:ComputeπbyaMonteCarlomethod........... 507
Exercise8.28:ComputeπbyaMonteCarlomethod........... 508
Exercise8.29:Computeπbyarandomsum .................. . 508
Exercise8.30:1Drandomwalkwithdrift..................... 508
Exercise8.31:1Drandomwalkuntilapointishit............. 508
Exercise8.32:Simulatemakingafortunefromgaming ......... . 508
Exercise8.33:Makeclassesfor2Drandomwalk............... 509
Exercise8.34:2Drandomwalkwithwalls;scalarversion ....... . 510
Exercise8.35:2Drandomwalkwithwalls;vectorizedversion.... 510
Exercise8.36:Simulatemixingofgasmolecules ............... . 510
Exercise8.37:Simulateslowmixingofgasmolecules........... 511
Exercise8.38:Guessbeerbrands............................ 511
Exercise8.39:Simulatestockprices.......................... 512
List ofExercises
xxix
Exercise8.40:Computewithoptionpricesinﬁnance........... 512
Exercise8.41:Diﬀerentiatenoisemeasurements ............... . 513
Exercise8.42:Diﬀerentiatenoisysignals...................... 514
Exercise8.43:Modelnoiseinatimesignal.................... 515
Exercise8.44:SpeedupMarkovchainmutation............... 516
Exercise9.1:Demonstratethemagicofinheritance ............ . 585
Exercise9.2:Makepolynomialsubclassesofparabolas ......... . 585
Exercise9.3:Implementaclassforafunctionasasubclass ..... . 586
Exercise9.4:Createanalternativeclasshierarchyforpolynomials 586
Exercise9.5:Makecircleasubclassofanellipse............... 586
Exercise9.6:Makesuper-andsubclassforapoint............. 586
Exercise9.7:Modifyafunctionclassbysubclassing............ 587
Exercise9.8:Exploretheaccuracyofdiﬀerenceformulas ....... . 587
Exercise9.9:Implementasubclass .......................... . 587
Exercise9.10:Makeclassesfornumericaldiﬀerentiation........ 588
Exercise9.11:Implementanewsubclassfordiﬀerentiation...... 588
Exercise9.12:Understandifaclasscanbeusedrecursively..... 588
Exercise9.13:Representpeoplebyaclasshierarchy ........... . 588
Exercise9.15:Computeconvergenceratesofnumericalintegration
methods .................................... . 590
Exercise9.17:Makeaclasshierarchyforrootﬁnding .......... . 591
Exercise9.18:Makeacalculuscalculatorclass ................ . 592
Exercise9.19:Computeinversefunctions..................... 593
Exercise9.20:Makelinedrawingofaperson;program ......... . 593
Exercise9.21:Makelinedrawingofaperson;class............. 593
Exercise9.22:Animateapersonwithwavinghands............ 593
ExerciseA.1:Determinethelimitofasequence ............... . 621
ExerciseA.2:Computeπviasequences ...................... . 622
ExerciseA.3:Reducememoryusageofdiﬀerenceequations..... 622
ExerciseA.4:Computethedevelopmentofaloan ............. . 623
ExerciseA.5:Solveasystemofdiﬀerenceequations............ 623
ExerciseA.6:Modifyamodelforfortunedevelopment ......... . 623
ExerciseA.8:Constructtimepointsfromdates................ 624
ExerciseA.9:VisualizetheconvergenceofNewton’smethod .... . 624
ExerciseA.10:Implementthesecantmethod.................. 625
ExerciseA.11:Testdiﬀerentmethodsforrootﬁnding.......... 625
ExerciseA.12:MakediﬀerenceequationsfortheMidpointrule.. 626
ExerciseA.13:Computethearclengthofacurve.............. 626
ExerciseA.14:Finddiﬀerenceequationsforcomputingsinx .... . 627
ExerciseA.15:Finddiﬀerenceequationsforcomputingcosx.... 628
ExerciseA.16:Makeaguitar-likesound...................... 628
ExerciseA.17:Dampthebassinasoundﬁle.................. 628
ListofExercises
ExerciseA.18:Dampthetrebleinasoundﬁle ................ . 629
ExerciseA.19:Demonstrateoscillatorysolutionsof(A.13) ...... . 629
ExerciseA.20:Automatecomputerexperiments............... 630
ExerciseA.21:GenerateanHTMLreport .................... . 630
ExerciseA.22:Useaclasstoarchiveandreportexperiments.... 631
ExerciseA.23:Explorelogisticgrowthinteractively............ 632
ExerciseA.24:Simulatethepriceofwheat.................... 632
ExerciseB.2:Studyafunctionfordiﬀerentparametervalues.... 660
ExerciseB.3:Studyafunctionanditsderivative .............. . 661
ExerciseB.4:UsetheTrapezoidalmethod.................... 661
ExerciseB.5:Computeasequenceofintegrals................. 662
ExerciseB.6:UsetheTrapezoidalmethod.................... 663
ExerciseB.7:Computetrigonometricintegrals ................ . 663
ExerciseB.8:Plotfunctionsandtheirderivatives.............. 664
ExerciseB.9:UsetheTrapezoidalmethod.................... 664
ExerciseC.1:SolveanonhomogeneouslinearODE ............ . 681
ExerciseC.2:SolveanonlinearODE......................... 681
ExerciseC.3:SolveanODEfory(x)......................... 682
ExerciseC.4:ExperienceinstabilityofanODE................ 682
ExerciseC.5:SolveanODEwithtime-varyinggrowth ......... . 682
ExerciseD.1:Modelsuddenmovementsoftheplate ........... . 710
ExerciseD.2:Writeacallbackfunction....................... 710
ExerciseD.3:Improveinputtothesimulationprogram......... 710
ExerciseE.1:SolveasimpleODEwithfunction-basedcode..... 758
ExerciseE.2:SolveasimpleODEwithclass-basedcode........ 758
ExerciseE.3:SolveasimpleODEwiththeODEsolverhierarchy. 758
ExerciseE.4:SolveanODEspeciﬁedonthecommandline ..... . 758
ExerciseE.5:ImplementanumericalmethodforODEs......... 759
ExerciseE.6:SolveanODEforemptyingatank .............. . 759
ExerciseE.7:SolveanODEforthearclength ................ . 760
ExerciseE.8:Simulateafallingorrisingbodyinaﬂuid........ 760
ExerciseE.9:Verifythelimitofasolutionastimegrows ....... . 762
ExerciseE.10:Scalethelogisticequation..................... 762
ExerciseE.11:Computelogisticgrowthwithtime-varyingcarrying
capacity .................................... . 763
ExerciseE.12:SolveanODEuntilconstantsolution........... 763