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PREFACE
Acollectionofsolvedproblemsinnumericalmethods,presentedinthistextbook,istheresultoftheauthors'
experienceofteachingtheundergraduatestudentsoftheFacultyofElectronicsandInformationTechnology
atWarsawUniversityofTechnologyintheperiod1985–2020,andinparticular–thestudentsfollowingthe
English-mediumprogrammesofstudyofferedthereduringlast25years.Itisassumedtobeacomplemen-
taryteachingmaterialwithrespecttothelecturenotes,distributedamongthestudentsatthebeginningof
eachsemester.Itmaybeusefulforstudentsattendinganyengineering-orientedcourseofnumericalmeth-
ods.Unlikecoursesofnumericalmethodsofferedtothestudentsofmathematicsandtheoreticalphysics,the
coursesdedicatedtostudentsofengineeringandappliedsciencesmustbeconciseandpracticallyoriented,
shouldcontainaverylimitedtheoreticalbackgroundandofferdiversifiedopportunitiesfordevelopingskills
necessaryforeffectiveandefficientapplicationofnumericalmethodsinprofessionalpractice.Unliketradi-
tionalcoursesofnumericalmethods,focusedonthedevelopmentofnumericalalgorithms“fromscratch”,
themoderncoursesdedicatedtostudentsofengineeringandappliedsciences,shouldenablethemtoreliably
usethelibrariesofnumericalalgorithms,suchastoolboxesofthecomputingenvironmentMATLAB.The
methodologicalassumptionsunderlyingsuchcourses–andconsequentlyjustifyingthecontentsofthistext-
book–arebrieflysummarisedintheparagraphstofollow.
Acreativeengineer–incontrasttoanengineeremployedasasalesman,clerkormanager–mustbepre-
paredtoreliablyevaluatenumericalalgorithmsinordertoproductivelyusetheminengineeringpractice
whichincludesdesigningandprototypingnewtechnicalobjects,aswellastheirtestingandmaintenance;all
beingtheoperationslargelysupportedbycomputers.Inthetimesofgrowingcomplexityoftechnicalobjects
andservicesdesignedaccordingtotechnoscientificmethodologies,knowledgeuncertaintyandtechnological
fallibilityaregettingtobecomethekeyconceptsofengineeringdesign.Evaluationofuncertainty,intro-
ducedbynumericalmethodsintodesignprocesses,seemstobe,therefore,afundamentalskillexpectedof
acontemporaryengineer.
Computersareomnipresentinourlives:weusethemtocreate,storeanddistributedocumentsinelectronic
formandtosearchthemontheinternet;tobookflightsandtheatretickets;toshopinonlinestoresandto
carryoutbankingtransactions.Computers,verydiversifiedifcomputingpowerisconcerned,areusedby
engineersnotonlyfordesigning,prototypingandtestingtechnicalobjects,butalsoforenablingorsupport-
ingtheoperationofthoseobjectsthemselves:cars,TVsets,refrigerators,etc.Implementationofallthose
functionsbycomputersinvolvestheuseofnumericalmethods,i.e.themethodsforapproximatelysolving
mathematicalproblems–ofalgebraical,analytical,statisticalorgeometricalnature–usingdigitaldevices
thatbyprincipleoftheirfunctioningcanaccuratelyperformonlylogicaloperations.Mathematicalmodelling
ofphysicalobjectsis,thus,akeytotheeffectiveuseofcomputersinengineeringtasks.Mathematicalmod-
ellingenablesustodescribeanobjectunderdesignwithmathematicalformulaewhichafteralgebraisation
becomethebasisforcomputersimulationofthebehaviourofthisobject.Theprinciplesofmathematical
modelling
1guaranteethepossibilityoftransferringtheconclusions,resultingfromsimulation,tothedesign
ofthephysicalobjectandtotheprocessofitsproduction.
1Formoredetails,seeChapter5ofthehandbookTechnoscientificResearchMethodologicalandEthicalAspects(DeGruyter,Berlin-Boston2019)
byRomanZ.Morawski.
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