[PDF] fonction maple
[PDF] dosage chlorure de sodium par nitrate d'argent
[PDF] argentimétrie dosage
[PDF] tp4 titrage par précipitation méthode de mohr
[PDF] dosage des chlorures par la méthode de mohr tp
[PDF] dosage argentimétrique des chlorures
[PDF] dosage des ions cuivre par spectrophotométrie
[PDF] dosage des ions sulfates par spectrophotométrie
[PDF] dosage du cuivre par l'edta
[PDF] iodometrie dosage du cuivre d'une solution de sulf
[PDF] dosage des ions cuivre ii corrigé
[PDF] tp dosage spectrophotométrique du cuivre
[PDF] dosage du cuivre par spectrophotométrie uv-visible
[PDF] oxydoréduction exercice
[PDF] exercices rédaction lettre commerciale
r=0tor=4. arrowoperator.Forexample,> statement> plot(area,0..4);
1 2 3 40
2+2> iquo(23,2);#dividestheintegers11 irem(23,2);#givestheintegerremainder1 4ya i:='i';#makesiavariableagaini:=i>
intoaninputcell,ifyouareexpectingoutput. x-3. thisistokeepaninputcellofvariablesused. inputcells. referencethelastcomputation. end;Thisoftenworks. yourworksheet. 26
outforyourinspection.quotesdbs_dbs7.pdfusesText_13
[PDF] dosage chlorure de sodium par nitrate d'argent
[PDF] argentimétrie dosage
[PDF] tp4 titrage par précipitation méthode de mohr
[PDF] dosage des chlorures par la méthode de mohr tp
[PDF] dosage argentimétrique des chlorures
[PDF] dosage des ions cuivre par spectrophotométrie
[PDF] dosage des ions sulfates par spectrophotométrie
[PDF] dosage du cuivre par l'edta
[PDF] iodometrie dosage du cuivre d'une solution de sulf
[PDF] dosage des ions cuivre ii corrigé
[PDF] tp dosage spectrophotométrique du cuivre
[PDF] dosage du cuivre par spectrophotométrie uv-visible
[PDF] oxydoréduction exercice
[PDF] exercices rédaction lettre commerciale
ProblemSolvingwithMaple
Ahandbookforcalculusstudents
CarlEberhart,carl@ms.uky.edu
SDTAntdef
SSTTOAFUNDFST
EXV1EXV2IV
ConprpsRULD
DIC MV IMVIntdefLimdefCondef
LUBDerdef
Limprps
CIIIntprps
December12,2003
Contents
1Raisond'Maple4
2AnintroductiontotheMaplelanguage9
3SettingUpandSolvingProblems28
4MoreworkedProblems41
5Dierentiationanditsuses.49
16MoreMax-minProblems59
7EarlyIntegration.67
7.5Modelingthe
8MomentsandCenterofMass77
9DenitionsandTheoremsofCalculusI80
10InverseFunctions83
11IntegrationTechniquesandApplications94
12Taylor'sTheorem104
213SequencesandSeries109
13.3.1TheSnow
14Dierentialequations121
31Raisond'Maple
1.1FourPropertiesofMaple
Forexample,thecommand>
displayed). 4 language,andfosterourexperimentalurges.3*(4+5*3)*(7+6;Syntaxerror,`;`unexpected
occursandmakethecorrection s:=3^23+4^12; ifactor(s);s:=94159956043 (727)(129518509)5 theinputcell,andreexecuteit. yourworksheetiftheneedarises.> plot(x^3-x+4,x=-2..2);±20246810 ±2±112x
plot(x^3-x+4,x=-2..2);±20246810
±2±112x
TextorCommentCells:
6 document.1.3Gettoknowthelanguage
,etc.YoucanlearnaboutthemwithonlineHelp.Forexample,tondoutaboutfactorjusttype>
examplesoftheusageoftheword,inmanycases.1.3.1Problems:
71.4Experiment!
1.4.1Problems
example(list); intheexamplesheetforsetandlist. 82AnintroductiontotheMaplelanguage
2.1Arithmetic
2-3+4/5*6^7;1119739
5 isthesameasentering> (2-3)+(4/5)*(6^7);1119739 51/3+1/2;5
returnadecimalanswer.> entering> ofacircleofradius3,youwouldenter>Pi*3^2;99
whenris3,weenter> oftheradiusr.2.3Functions
numbers,butthenotionoffunctionismuchmore exiblethanthat.Asanexpression:Theassignment>
plot(area,r=0..4);1001020304050
1 234rr=0tor=4. arrowoperator.Forexample,> statement> plot(area,0..4);
01020304050
1 234Notethatthevariablerisomittedhere.
assignment> pol:=x^2+4*x-1;pol:=x2+4x111 thentheassignment> theprocedure,withtheMaplewordERROR. area:=proc(r)Pi*r^2fiend;area:=proc(r)
endproc> area(3);9>Notetheif..then..controlstatementhere.
plot3d(V,0..4,0..4,axes=boxed);12 0 1 2 3 401 2 3 40
50100150200
moreandmoreastimegoesby.Piecewisedenedfunctions:
Hereisanexampletoshowusage.>
cos(x),3*x);f(x):=8 :x 3+8x17+2xx2
11cos(x)x4
3xotherwise>
f(2);f(2) g(2);11 plot(g,-3..6,style=point);±15±10±5051015
±2246
13 infunctions,type> thex-axis.> f:=x->10*x^5-30*x+10;f:=x!10x530x+10> plot(f,-3..3);±2000±1000010002000 ±3±2±1123
14 plot(f,-1.5..1.5);±20±10010203040±1.5±1±0.50.511.5
asolution.> whattype(1/2);fraction> whattype(a+b);+ whattype(x^2+x=2*x-1);= example,> ;x+(sin@cos@(x!x2+3))z 15 viola[6];x+(sin@cos@(x!x2+3))z List. ;x+(sin@cos@(x!x2+3))z nops(explist);7 list.Thisdeviceisusedagainandagain.> nops([3,4,a]);3 multipliedbyanumber.> p:=[1,2];q:=[-3,1];p:=[1;2] q:=[3;1]> plot(ab);1611.522.53
11.522.53
restrictingthexandycoordinates.> plot([1+4*cos(t),5+4*sin(t),t=0..Pi], scaling=constrained); 6789±2024
thesequenceoflists> cos(t);1+12 sin(t);t=0::2];[3+12 cos(t);1+12 sin(t);t=0::2]; [3+12 cos(t);3+12 sin(t);t=0::2];[1+12 cos(t);3+12 sin(t);t=0::2]17 0.511.522.533.5
tosplitofromabtheoddandeventerms{> wecangetittodowhatwewant.> plot(newab,color=black);181.522.53
±10
±8±6±4±20246810
Sets listit.> plot(fx^2-2,2*x+5g,x=-5..5);±505101520
±4±224x
youhavenamed. 19 pl1:=plot(fx^2-2,2*x+5g,x=-5..5): pl2:=plot([[2,1],[3,20],[0,0],[2,1]]): plots[display]([pl1,pl2]);±505101520 ±4±224x
TablesandArrays
exible.Thepackagesofspecial exceptforarrays. multiplication&*.> sincos#> ang:=evalf(Pi/180*31);ang:=0:5410520681> [0:3421292258;1:372205376]]20 plot(f[[0,0]],ab,rotabg);01234±0.50.511.522.53
2.7Maplecontrolstatements
for..from..by..to..while..do..od; aniterativealgorithm.Example:Adduptherst100numbers.>
s:=0:forifrom1to100dos:=s+iod: s;5050 doitagain,storingtheminanarray.Solutionwithlists:>
locube:=NULL:#startwiththeemptyexprseq forifrom1to5do locube:=locube,i^3od:Solutionwitharrays:>
aocube:=array(1..5):#initializethearray. aocube2:=8 aocube3:=2721 aocube4:=64 aocube5:=125> aocube[3]:=0;aocube3:=0> print(aocube);[1;8;0;64;125]> if..then..elif..else..;Asolution:>
myabs(-23);23 toseewhatitlookslike.22 my absolute value00.511.52
±2±112
2.8ABriefVocabularyofMapleWords
browser.>D(cos);#thedifferentialoperatorsin>
y:='y';#makesyavariableagain.y:=y> expand((x+b)^7);#expandstheproductxInt(x*exp(x),x=0..1);#Apassiveintegral.Z
10xexdx>
±3±2±1123x>
f(3);#thenreturns9.9 242+2> iquo(23,2);#dividestheintegers11 irem(23,2);#givestheintegerremainder1 4ya i:='i';#makesiavariableagaini:=i>
2.9TroubleShootingNotes
workinglikeitshould. plotx^2;Error,missingoperatoror`;` 25intoaninputcell,ifyouareexpectingoutput. x-3. thisistokeepaninputcellofvariablesused. inputcells. referencethelastcomputation. end;Thisoftenworks. yourworksheet. 26
outforyourinspection.quotesdbs_dbs7.pdfusesText_13