工程力学专业本科课程描述(英文版)Course descriptionx.docx
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工程力学专业本科课程描述(英文版)Course descriptionx.docx
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SOUTHEASTUNIVERSITY
SchoolofCivilEngineering
CourseDescriptions
UndergraduateStudiesofEngineeringMechanics
August2016-Present(3AcademicYears)
1BasicCoursesofNaturalSciences
ØAdvancedMathematics(A)I
Coursecontents
1)Preparatoryknowledge:
sets,neighborhoods,functionsandtheirproperties,etc.
2)Univariatefunctiondifferentialcalculus:
limitsofsequencesandfunctions;propertiesandcomputationoflimits;limitexistencecriteria;functioncontinuity;computationofderivatives(includinghigh-orderderivatives);applicationofderivatives;differentialanddifferentialmeanvaluetheorem;L'Hospital’sLaw;Taylor'sFormula,etc.
3)Integraltheory:
indefiniteintegral;integrationbysubstitutionandsubsection;definiteintegral;geometricalandphysicalapplicationofintegral;generalizedintegralanditsconvergenceanddivergence,etc.
4)Ordinarydifferentialequations:
solvingmethodsforfirst-orderequations,second-orderdegradableequations,andhigh-orderlinearequations,etc.
5)Seriestheory:
numberseries,functionseries,powerseries,Fourierseries,andtheirpropertiesandconvergencecriteria;conceptsofabsoluteconvergenceandconditionalconvergence;Taylorseriesexpansionoffunctions,etc.
Thiscoursealsoincludesamathematicalexperimentassignment.
Duration:
16weeks
Hours:
6hours/week
ØAdvancedMathematics(A)II
Coursecontents
1)Limitsandcontinuityofmultivariatefunctions.
2)Differentialofmultivariatefunctions:
partialderivatives;directionalderivativesandgradients;totaldifferential;differentialofvector-valuedfunctions;implicitfunctiontheorems;Taylor’sformula;extremumandconditionalextremumofmultivariatefunctions,etc.
3)Concepts,propertiesandcalculationmethodsofmultipleintegrals;geometricalandphysicalapplicationofmultipleintegrals,etc.
4)Parametricintegral;curveandsurface,andtheirorientation;curveandsurfaceintegrals,etc.
5)PlanarvectorfieldandGreenformula;spatialvectorfieldandGaussformula,Stokesformula;path-independentintegraltheorem,etc.
6)Complexvariablefunctions:
definitionandpropertiesofanalyticfunctions;Cauchy-Riemannequation;Cauchyintegraltheoremofanalyticfunctions;classificationofsingularitiesofcomplexfunctions;Laurentseries;residualtheorem,etc.
Thiscoursealsoincludesamathematicalexperimentassignment.
Duration:
16weeks
Hours:
6hours/week
ØGeometry&Algebra(B)
Coursecontents
1)Theoryofdeterminant:
definitionofpermutationanddeterminant;propertiesofdeterminant;Laplaceexpansiontheorem;Gramer'slaw;calculationofdeterminants,etc.
2)Theoryofmatrix:
definitionandoperationofmatrix;Binet-CauchyFormula;elementarymatricesandelementarytransform;nonsingularmatrix;rankofmatrices;blockmatrix,etc.
3)Linearequations:
theGausseliminationmethod;basicsolutionsystemandsolutionspace,etc.
4)Vectorsingeometricspace:
linearoperations;dotproductandcrossproductofvectors;equationsofspatialplanesandlines;spatialdistance,etc.
5)Linearspaceandlineartransformation:
definitionoflinearspace,linearcorrelation,andlinearindependence;subspace;basisandcoordinates;coordinatetransformation;similarityofsquarematrices;eigenvaluesandeigenvectors;eigenspace;diagonalizationofmatrices;lineartransformation,etc.
6)Quadraticform:
orthogonality;standardorthogonalbasis;orthogonalmatrix;standardformofaquadraticform;positivedefiniteinnerproductandinnerproductspaceofrealquadraticformand
realsymmetricmatrix;linearfunctionandadjointtransformation;orthogonaltransformation;positivedefinitematrix;orthogonalsimilarity;spatialquadraticsurfaces,etc.
Duration:
16weeks
Hours:
4hours/week
ØTheoryofProbability&MathematicalStatistics(A)
Coursecontents
1)Randomevents;probabilityandprobabilityspaces;conditionalprobabilityandindependentevents;independentrandomtrials,etc.
2)Discrete,continuous,andmultidimensionalRandomvariablesandtheirdistributions;severalimportantcommonprobabilitydistributions(Bernoullidistribution,Poissondistribution,normaldistribution,etc.)andtheirproperties;conditionaldistributionandindependence;distributionofrandomvariablefunctions,etc.
3)Probabilitymeasureintegralanditsproperties(includingintegraltransformationtheorem);expectationandvariance,andtheirproperties;multivariatenormaldistributionanditsproperties;samplingdistributiontheorem,etc.
4)Probabilitylimittheory(including4kindsofnecessaryandsufficientconditionsforconvergenceandtheirrelations);B-Clemma;ChebyshevinequalityandKolmogorovmaximuminequality;thecentrallimittheoremandthelawoflargenumbers,etc.
5)Generalconfidenceintervals,inparti
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