麻省理工開放課程：多變量微積分 Multivariable Calculus 英文版 DVD 只於電腦播放 課程介紹： 本課程內容包括向量和多變量微積分,屬於是一年級第二學期微積分課程。主題包括向量和矩陣，偏導數，雙重和三重積分，平面和空間微積分。 麻省理工學院開放式課程提供了另外2006年春季的18.02版本。這兩個版本使用相同的內容，他們是由不同的教師授課，並依賴於不同的教科書。多變量微積分（18.02）是麻省理工學院秋季和春季的任教課程，是麻省理工學院所有本科生必修科目。 導師介紹 DenisAurouxreceivedtheMa?triceinmathematicsfromtheécoleNormaleSupérieure,ParisVIIin1994,theLicenceinphysicsfromParisVIin1995,theDiplomainmathematicsfromtheUniversitédeParisSud,1995,andthePh.D.fromécolePolytechniquein1999.Jean-PierreBourguignonandMishaGromovwerehisdoctoraladvisors.HecompletedthehabilitationattheUniversityofParisSudin2003.HecametoMITasaCLEMooreinstructorin1999andjoinedtheMITmathematicsfacultyin2002.Hewaspromotedtoassociateprofessorin2004andtenuredin2006.ProfessorAuroux'sresearchinterestsareinthefieldsofsymplectictopologyandmirrorsymmetry.HisdistinctionsincludethePrixdeThèse,écolePolytechnique,1999;thePrixPeccot&CoursPeccot,CollègedeFrance,January2002,andtheAlfredP.SloanResearchFellowship,2005.HereceivedtheMITSchoolofSciencePrizeforExcellenceinUndergraduateTeachingin2006. 目錄: Lecture01:Dotproduct Lecture02:Determinants;crossproduct Lecture03:Matrices;inversematrices Lecture04:Squaresystems;equationsofplanes Lecture05:Parametricequationsforlinesandcurves Lecture06:Velocity,acceleration;Kepler'ssecondlaw Lecture07:Review Lecture08:Levelcurves;partialderivatives;tangentplaneapproximation Lecture09:Max-minproblems;leastsquares Lecture10:Secondderivativetest;boundariesandinfinity Lecture11:Differentials;chainrule Lecture12:Gradient;directionalderivative;tangentplane Lecture13:Lagrangemultipliers Lecture14:Non-independentvariables Lecture15:Partialdifferentialequations;review Lecture16:Doubleintegrals47:59DenisAuroux Lecture17:Doubleintegralsinpolarcoordinates;applications Lecture18:Changeofvariables Lecture19:Vectorfieldsandlineintegralsintheplane Lecture20:Pathindependenceandconservativefields Lecture21:Gradientfieldsandpotentialfunctions Lecture22:Green'stheorem Lecture23:Flux;normalformofGreen'stheorem Lecture24:Simplyconnectedregions;review Lecture25:Tripleintegralsinrectangularandcylindricalcoordinates Lecture26:Sphericalcoordinates;surfacearea Lecture27:Vectorfieldsin3D;surfaceintegralsandflux Lecture28:Divergencetheorem Lecture29:Divergencetheorem(cont.):applicationsandproof Lecture30:Lineintegralsinspace,curl,exactnessandpotentials Lecture31:Stokes'theorem Lecture32:Stokes'theorem(cont.);review Lecture33:Topologicalconsiderations;Maxwell'sequations Lecture34:Finalreview Lecture35:Finalreview(cont.)