MuPAD部分命令学习.docx
《MuPAD部分命令学习.docx》由会员分享，可在线阅读，更多相关《MuPAD部分命令学习.docx（35页珍藏版）》请在冰豆网上搜索。
MuPAD部分命令学习
GettingStartedwithMuPAD
ThisguideisintendedtoquicklygetyoufamiliarwiththewaythatMuPADworks.MuPADhasmanyfeaturesthatwecannotcoverinashortguide,buttheguideshouldbeenoughtogetyoustarted.Theprogramhasaveryniceon-linehelpfacilityformoredetailedinformation.YoushouldworkthroughthisguidebycopyingthecommandsintoMuPAD.Youcouldretype,orjustusecopyandpaste.
Contents:
MuPADasacalculator
GettingHelp
SymbolicCalculations
SavingYourWork
Variables
Functions
PlottingGraphsofFunctions
Differentiation
Integration
SolvingEquations
SolvingInequalities
Limits
ComplexNumbers
Sums（orSeries（级数））
PowerSeries（幂级数）
MatricesandVectors
Sequences,ListsandSets
Libraries
MoreonMatricesandVectors
Exportthelinearalgebralibrary
MoreGraphics
DifferentialEquations
NumericalSolutionofODEs
ElementsofProgramming
MuPADignorescomments
MuPADasacalculator
Enterthefollowing.Youcouldcopyandpasteintomupad,orretype.
354/36
MuPADlikestodoexactcalculations.Youcangetapproximateresultsbyusingfloat:
float（%）
Thesymbol%referstotheresultofthelastcalculation.Similarly%2,%3,etc.refertothesecond-to-last,third-to-lastandsoon.
sqrt（%2）
Thiscan'tbeevaluatedexactlysomupadjustrationalises（合理的说明）thedenominator（分母）.Youcanfurthersimplifyexpressionsusingmupad'ssimplify:
simplify（%）
Ifthere'sadecimalpointinanexpressionthenmupadtreatsitasbeingapproximateandgivesananswerintermsof（依据）decimals:
sqrt（118.0/69）,sqrt（118/69）
MuPADhasallthemathematicalfunctionsandoperationsthatyoufindonacalculator,andmanymore:
3!
exp
（1）,ln（2.3）,sin（PI/4）,log（2,16）,cos（PI/3）,arctan
（1）
Someotherusefulfunctionsarefloor,ceil,frac.
floor（x）isthegreatestintegerlessthanorequaltox.
ceil（x）istheleastintegergreaterthanorequaltox.
frac（x）isthefractionalpart（小数部分）ofx.
Simicolons（分号）betweenexpressionsyieldoutputondifferentlinesbutcommas（逗号）keeptheoutputonthesameline.Infact,commasareusedtoputthingsinasequence,so3^（1/2）,4isregardedasonepieceofoutput（asequence）inthefollowing.
3;sqrt（3）,4;2^3
Acolonsuppresses（抑制,禁止）theprecedingoutput,Quiteusefulfordoingabunchofcalculationsinonestep:
4:
2^3
GettingHelp
TherearetwowaystouseMuPAD'sHelpfeature.TofindoutmoreaboutaMuPADfunctionjustenter?
followedbythefunctionname.
Trythis:
?
log
Theotherwaytogethelpisthroughthehelpmenu.ThisstartsahelpbrowserthatletsyousearchforinformationaboutMuPAD.
SymbolicCalculations
Thefunctionsexpand,simplify,normalandfactorareveryusefulformanipulating（
处理,化简）expressions:
expand（（2+x）^3-（5+2*x）^2+17）
factor（%）
simplify（（2*x^2+3*x+1）/（x+1）^2）
Thefunctionnormalrewritesarationalexpression（有理表达式）asasinglefraction（分数）:
normal（2/x+3*（x+1）/（x^2+1））
simplify（sin（x）^2+cos（x）^2）
SavingYourWork
TheFilemenuofMuPADLightallowsyoutosaveyoursessionasatextfile.Thiscanbeopenedwithatexteditor（suchasTextPadifyouuseaPC）,orawordprocessingprogram（suchasMSWord）.Youcouldalsojustcopyandpasteeverythingintoawordprocessingprogram（文字处理程序）.IfyouneedtouseyourMuPADstatementsagain,justcopyandpastebackintoMuPAD.MuPADLightusesaprogramVCAMLighttodisplaygraphics.YoucancopyandpastegraphicsintoaMSWorddocumentaswell.MuPADProuserscandothesethingsaswellbutthisprogramallowsuserstosavetheirworkandgraphicsinnotebooks.
Variables
Avariablecanbeassignedavaluebyusingthesymbol:
=
x:
=2
2*x^2+y
y:
=5
IfyouaskMuPADforthesecond-to-lastoutput,itwon'tevaluateitwiththenewvalueofy
%2
butyoucanaskittoevaluateitwiththeevalcommand.
eval（%）
VariablesneednotjusthavenumericalvaluesinMuPAD.TheycanbeequatedtoanyMuPADexpression.
B:
=z^2+5*z+1
Wecouldsubstitute（代替,替换）thevaluez=5intothisexpressionusingMuPAD'ssubscommand:
subs（B,z=5）
Youlistallofthevariablesthatyouareusingwiththefunctionanames.
anames（All,User）
Variablescanbedeletedfrommemoryandyou'llneedtodothisfromtimetotime（不时的）whenyouusevariablesfordifferentthings.
deleteB,y:
NowifweenterthesevariablesthenMuPADjustdisplaystheirsymbolsbecausetheydon'thavevalues.
B,y
Functions
WehavealradyseenthatMuPADhaslotsofbuilt-infunctions.Wecanalsobuildourownfunctions.
e.g.Thefunctionf（x）=x^2+1canbethoughtofasanoperationthatmapsanumberxtoanumberx^2+1,i.e.x->x^2+1.
f:
=x->x^2+1
f
（2） ,f（a）
CompositionoffunctionsishandledwithMuPAD's@operator.Asanexample,tocompute
with
g:
=x->2*x:
justdothis:
h:
=f@g
h（3）
Alternatively,youcoulddefinehmoreexplicitly（明确地,明白地）:
h:
=x->f（g（x））
Functionsoftwoormorevariablescanbewrittenlikethis:
g:
=（x,y）->x*y
g（2,5）
It'seasytowritepiece-wisedefinedfunctions（分段函数）inMuPAD.Forexample,let'senterthefollowingfunctionintoMuPAD:
f:
=x->piecewise（[x<-1,x+2],[x>=-1andx<3,1],[x>=3,x^2]）
PlottingGraphsofFunctions
Functionsareeasilyplottedwithplotfunc2d.
plotfunc2d（sin（x）,cos（x）,x=-PI..PI）
Wecanalsospecifytheplotrangeinthey-directionandthenumberofpointsusedtocreatethegraph:
plotfunc2d（（x+1）/（x^2-5）,x=-8..8,y=-10..10）
Thedefaulttitleofagraphisjustthemathematicalexpressionforwhatisbeinggraphed.ButyoucanchangethiswiththeTitleoption:
f:
=x->piecewise（[x<-1,x+2],[x>=-1andx<3,1],[x>=3,x^2-8]）:
plotfunc2d（f（x）,x=-3..4,Title="Graphoff（x）"）
Youcanalsochangetheaxislabels.Forexample,toplottherelationw=t^2,withfancyaxislabels,dosomethinglikethis:
plotfunc2d（t^2,t=-2..2,AxesTitles=["timet（hours）","distancew（metres）"]）
Youcanplot functionsoftwovariableswithplotfunc3d:
plotfunc3d（1-x^2-y^2,x=-2..2,y=-2..2）
Youcanevenplotanumberoffunctions,aswellasspecifyingthenumberofgridpointsfortheplot,andthepointfromwheretheplotisviewed:
plotfunc3d（1-x^2-y^2,3-2*x-2*y,x=-2..2,y=-2..2,Mesh=[20,30],CameraDirection=[-20,5,0]）
Differentiation
Thefunctiondiffdifferentiates:
diff（x^3,x）
Higherorderderivatives（高阶微分）arecomputedlikethis4thderivative:
diff（exp（a*x）,x$4）
ButMuPADalsounderstandsprimenotationforderivatives.
sin'（x）
g:
=x->3*cos（x^2+1）:
g''（x）
Partialderivatives（偏微分）arehandledwithdiff.Forexample,tocalculate
enterthefollowing:
diff（h（x,y）,x$2,y$3）
Theoutputshowsanotherwaytoenterpartialderivatives.
diff（h（x,y）,x,x,y,y,y）
Integration
Useintforindefiniteordefiniteintegrals（定积分）:
int（1/sqrt（1-x^2）,x）
Thisistheantiderivative（原函数,反导数）.
Don'tforgettoincludeanarbitraryconstant（任意常数）!
Tocalculate
justdothis:
int（1/sqrt（1-x^2）,x=0..1）
Infinityisrepresentedbyinfinity:
int（1/（1+x^2）,x=-infinity..infinity）
Sometimesthereisnoniceexpressionforanintegral.Inthiscase,MuPADjustreturnstheformulathatyougaveit.Butyoucouldstillgetanumericalapproximation（近似值）toadefiniteintegral.
int（exp（-x^3）,x=0..3）
float（%）
Ifyou'recalculatingintegralsusingpartialfractions（部分分式,）,you'llfindthepartfracfunctionhandy（很方便的）:
partfrac（（2*x^3+3*x+1）/（（x+1）*（x+2）^2）,x）
SolvingEquations
z:
=solve（（x^2+2*x+2）/（x+3））
Therearetwosolutions.Topickoutthefirstsolution,trythis:
z[1]
solve（tan（y）=1,y）
Thisexampleinvolvesanarbitraryconstantthatbelongstothesetofintegers（整数集）（Z_inMuPAD）.MuPADdenotes（表示）arbitraryconstantswithsymbolsX1,X2,X3,etc.
Tosolveasystemofequations,enclosetheequationsandthevariableswithcurlybraces（大括号）:
solve（{2*x^2+y=5,x+3*y=10},{x,y}）
solve（a*x^2+b*x+c=0,x）
NoticethatMuPADlistsallpossiblecases:
Thesetofallcomplexnumbersifa,bandcareallzero;theemptysetifaandbarezeroandcisnotzero;-c/bifa=0andbisnotzero;andtheusualsolutiontothequadraticequation（二次方程式）ifaisnon-zero.IfwetellMuPADthataisnotzerothenthesolutionsimplifies:
assume（a<>0）:
solve（a*x^2+b*x+c=0,x）,unassume（a）
SolvingInequalities
Thefunctionsolvealsosolvesinequalities.
solve（2*x^2-5*x+3>=0,x）
Oneuseforthisistofindoutwhereafunctionisincreasing.
f:
=x->（2*x+1）/（3*x+5）
solve（f'（x）>0,x）,simplify（%）;/*此应该用simplifyp化简命令化简，MATLAB中还有一个simple也可以化简。
*/
Anotherexample:
solve（{3*x+1<0,2*x+5>0},x）
Limits
limit（sin（x）/x,x=0）
limit（（3*x^2+6）/（2*x^2+sin（x））,x=infinity）
limit（x/abs（x）,x=0）
Leftorrightlimitsmayexisteveniftheactuallimitdoesnot,andtheyareeasytocompute:
limit（x/abs（x）,x=0,Left）,limit（x/abs（x）,x=0,Right）
ComplexNumbers
MuPADdenotesi=sqrt（-1）withthesymbolI.
solve（x^2+x+1=0,x）
Thefunctionrectformexpressesacomplexnumberintheformx+Iy.
rectform（z）:
computestherectangularformofthecomplexexpression,itsplits（分裂）into
.将复数转化成直角坐标的形式,即
的形式.
rectform（ln（1+I））
Realandimaginaryparts（实部与虚部）ofcomplexnumbers（复数）arefoundwithReandImandtheconjugate（共轭复数）withconjugate.
Re（%）,Im（3+2*I）,conjugate（4+7*I）
Theabsolutevalueofacomplexnumberisfoundwithabsandtheargument（辐角）witharg:
abs（1+5*I）,arg（2+I）
Sums（orSeries（级数））
Tocompute
useMuPAD'ssumfunction:
sum（1/n^2,n=1..infinity）
sum（k,k=1..n）
sum（n*exp（-n）,n=1..5）
sum（sin（n）/n,n=1..infinity）
Althoughtheanswerisreal,it'swrittenintermsofcomplexnumbers.Userectformtogetanexpressionwhichdoesn'tinvolvecomplexnumbers.
rectform（%）//将一个复数化为x+iy形式，若没用y，也就说明这个数是实数;
SometimesMuPADcan'tgiveaniceexpre
升级会员 