复旦大学《大学物理》课件（英文）-第0、1章(1).pdf

Chapter 1Chapter 1 MeasurmentIntroduction to PhysicsIntroduction to Vectors Introduction to Calculus(微积分)Chapter 0 PrefaceChapter 1Chapter 1 MeasurmentChapter 0 PrefaceIntroduction to Physics1)Objects studied in physics2)Methodology for studying physics3)Some other key points(See 动画库力学夹绪论.exe)Chapter 1Chapter 1 MeasurmentChapter 0 PrefaceIntroduction to VectorsA scalar is a simple physical quantity that does not depend on direction.mass,temperature,volume,workA vector is a concept characterized by a magnitude and a direction.force,displacement,velocityChapter 1Chapter 1 MeasurmentChapter 0 Preface1)Representationof vectors2)Addition and subtraction of vectors3)Dot and cross products(See 动画库力学夹0-4矢量运算.exe)(See 动画库力学夹0-4矢量运算.exe)Chapter 1Chapter 1 MeasurmentABAB?Chapter 0 Preface)(|cos|BABA=3.1)Dot product:ABAB)(Bcos)(AcosNo problem，if Chapter 1Chapter 1 MeasurmentChapter 0 PrefacekAjAiAAzyx+=kBjBiBBzyx+=?=BA)BBB()(kjikAjAiABAzyxzyx+=zzyyxxBABABA+=zzyyxxBABABABA+=ABBA=22A|AAA=|CABACBA+=+)(Prove it?Chapter 1Chapter 1 MeasurmentChapter 0 Preface3.2)Cross product:nABsinBA)(=is a unit vector perpendicular to both and .,and also becomes a right handed system.nnThe length of can be interpreted as the area of the parallelogram having A and B as sides.ABABABABBAnBA-AB=AB|BA|,BA If0BA,B/A If=Scalar triple product:?)(=CBA Chapter 1Chapter 1 MeasurmentChapter 0 PrefacekAjAiAAzyx+=kBjBiBBzyx+=?=BA)BBB()(kjikAjAiABAzyxzyx+=jBABAiBABAzxxzyzzy)()(+=kBABAxyyx)(+zyxzyxBBBAAAkjiBA=jBABAzxxz)(+kBABAxyyx)(+iBABAyzzy)(=Chapter 1Chapter 1 MeasurmentChapter 0 PrefaceIntroduction to Calculus(微积分)1)Limit of a function Lxfcx=)(lim(x)can be made to be as close to L as desired by making x sufficiently close to c.“The limit of of x,as x approaches c,is L.Note that this statement can be trueeven if or(x)is not defined at c.Lcf)(11)(2=xxxfExample:2|1)(lim11=+=xxxxfChapter 1Chapter 1 MeasurmentChapter 0 Preface2)Derivative of a function(函数的导数)Motion with constantvelocitytst1t21212)()()(tttststv=tst1t2 Motion with changingspeed1212)()()(tttststv=?Chapter 1Chapter 1 MeasurmentChapter 0 PrefaceHow to find the instantaneous speed at t1?12121)()(lim)(12tttststvtt=Motion with changing speedttsttstvt+=)()(lim)(0tt=1ttt+=2dtds=Derivative of sChapter 1Chapter 1 MeasurmentChapter 0 PrefaceFor general function,its derivative is defined as:xxfxxfdxxdfx+=)()(lim)(0)(yxfxf(x)x1x2AAtangentThe meaning of derivative of a function:xy=tan10limtanlimxxAAxy=AA)(1xftan=tan)(1=xfChapter 1Chapter 1 MeasurmentHow big is an infinitesimal?.0 xis infinitesimal.xChapter 1Chapter 1 MeasurmentChapter 0 PrefaceChapter 1Chapter 1 MeasurmentChapter 0 PrefaceExample:2xy=xxxxxxxxxxxfxxfyxxx22lim)(lim)()(lim202200=+=+=+=Some basic formulae:0)(=cxxee=)(1)(=xx)(numberrealaisxxcos)(sin=xxsin)(cos=xx1)(ln=Chapter 1Chapter 1 MeasurmentSome basic rules:Chapter 0 Preface)(vuvu=)(uvvuuv+=)0()(2=vvuvvuvu=)(),(xvvfy)()()(xvvfxy=dxdvdvdydxdyor=For a vector:kdtdAjdtdAidtdAdttAdzyx+=)()(CuCu=,C is a const.Chapter 1Chapter 1 MeasurmentChapter 0 Preface3)Differential of a function(函数的微分)If f(x)has its derivative at point x,then f(x)dx is its differential at that point.dxxfdy)(=dxDifferential of the functionDifferential of the variableSo f(x)is also called differential quotient(微商)dxdy=Chapter 1Chapter 1 MeasurmentChapter 0 Prefacedvduvud=)(udvvduuvd+=)()0()(2=vvudvvduvudCduCud=)(,C is a const.Operation rule is the same as that for derivative:.One application of differential)()()(000 xxxfxfxfy=0 xxif)()()(000 xxxfxfxf+00=xWhenxffxf)0()0()(+Chapter 1Chapter 1 MeasurmentChapter 0 PrefaceExample:0,)0cos(|)(sin)0sin()sin(0=+=xxxxxxxFollowing approximate formulae often used in physics():xx)sin(NxxN+1)1(xx2111+xx+)1ln(xex+1xx)tan(.0 xxffxf)0()0()(+Chapter 1Chapter 1 MeasurmentChapter 0 Preface4)Integrals(积分)Motion with constantvelocity Motion with changing speed0vtS=tvt00Stvt00SHow to find S?Chapter 1Chapter 1 MeasurmentChapter 0 Prefacetvt00tittvttvttvSN+)(.)()(21=NtifttvNii,0,)(1=0010)()(limtNiiNtdttvttvSIn general,the integral from a to b of f(x)with respect to x is expressed as:badxxf)(definite integral dxxf)(indefinite integral Chapter 1Chapter 1 MeasurmentChapter 0 PrefaceHow to find an integral of a function?)()()(abxdba=If function f(x)is continuous on the interval a,b and if on the interval(a,b),then)()(xfx=bababadxdxxddxxdxxf)()()()()(),()()(xfxabdxxfba=)()(,)()(xfxCxdxxf=+=Chapter 1Chapter 1 MeasurmentChapter 0 PrefaceExample:?121=dxxxx1)(ln=xxln)(=2ln|ln12121=xdxxBasic integral formulae:+=Cxdx+=Ckxkdx+=Cxxdxsincos+=Cxxdxcossin+=Cedxexx+=Cxdxxln1)1(,11+=+aCaxdxxaak,C:const.Chapter 1 MeasurementDespite the mathematical beauty of some of its most complex and abstract theories,physics is above all an experimental science.1-1 Physical quantities,standards and units What will be measured?Physical quantities:mass,length,time,force Whats the standard for a measurement?Maintaining and developing standards is an activebranch of science.UnitsThere are seven kinds of base units in SI system.1-2 The