Matlab及其在数学建模中的应用

23120052()JournalofGuizhouNormalUniversity(NaturalSciences)Vol.23.No.1Feb.2005:10045570(2005)01-0077-05Matlab3,(,550001):,Matlab;Matlab,,:;Matlab:O29:AStudyofMatlabanditsapplicationinmathematicalmodelingSHANGYue2qiang,YANGYi2du(SchoolofMathematicsandComputerScience,GuizhouNormalUniversity,Guiyang,Guizhou550001,China)Abstract:Thispaperexplainsthegeneralprocessofmathematicalmodeling,studiesthefunctionandcharacteristicofMatlabanditsapplicationinmathematicalmodeling.Itcanimprovetheefficiencyandqualityofmathematicalmodeling,enrichthemeansandmethodsofmathematicalmodeling,andhasgreateffectontheteachingofmathematicalmodelingcourse.Keywords:mathematicalmodeling;Matlab20,,,,,,Matlab,,1,,:,,,,,,,,1[1]:(1):,,;(2):,,,,;(3):,,;773:2004-06-16:(1977-),,,,:(4):,;(5):,;(6):,,;,,;(7):,,,1Fig.1Thegeneralprocessofmathematicalmodeling2MatlabMatlab(MatrixLaboratory)Mathwork,,MapleMathmatica,[2]:(1):Matlab600,;6.5,(2),:Windows,Matlab,,;Matlab,(3),:Matlab,;Windows,,;,(4):6.5,(5):Matlab,,(6):Matlab,,M,(7):MatlabFORTRANCC++,3MatlabMatlab,,,,(Matlab6.5,,)1([3])100,,():,;10,167.8cm,,,(1):,,,,,,,(2):,;Matlab:clear%H=87()23[161175172172175175180179172174164170158176178178178171168169179163182174160163170160168176163170178178174172170170172180169171170168171179156158171171162175170170154175170168166164170168173162163160160172170172174172175160168170170158169173167164168170171176173169164167167168172163172164172168165160];H1=reshape(H,100,1);%hist(H1)%(2)[N,X]=hist(H1)%(1)2Fig.2Thestatisticalgraphofstudentsheight1100Tab.1Thefrequencytableof100studentsheightN239111318201383X155.4158.2161.0163.8166.6169.4172.2175.0177.8180.63Q2QFig.3TheQ2Qgraphinspectionofstudentsheight21:70%165175(cm),169(cm);,N(,2):,MatlabQQ:normplot(H1)%33,,:mean(H1)%median(H1)%std(H1)%Srange(H1)%skewness(H1)%g1kurtosis(H1)%g222100Tab.2thestatisticoftheheightof100students169.4400170.00005.946428.0000-0.32422.6849S=5.9464,g1=-0.3242,,0g2=2.6849,3,,:,,[musigmauncisigmaci]=normfit(H1,0.01),3(=0.01)3Tab.1Thepointandintervalestimationofthemeanandstandarddeviationofstudentsheight169.4400[167.8782,171.0018]5.9464[5.0187,7.2549]:971,:Matlab,:H0:=167.8;H1:167.8,t-,=0101[h,p,ci]=ttest(H1,167.8,0.01,1)h=1(H0),p=0.0035,ci=[168.0339,Inf]Matlab[4]Matlab,,,,,Matlab,(),,MatlabFORTRANCC++,,,,,,,,,,,,,,2[4],,,?(1):,3:;;(2):;(1)3(3)::P(/)L(/)W(/)abcx(/)y(/),:f(x,y)=(x-W)[L-a(P-y)+b(P-x)-c(x-y)],a,b,c0(4):[5],Matlab:symsLPWabcxyf=(x-W)3(L-a3(P-y)+b3(P-x)-c3(x-y));df=diff(f,x);%x0=solve(L-a3(P-y)+b3(P-x)-c3(x-y)+(x-W)3(-b-c)=0,x)%,f(x,y)x:x0=[L+y(a+c)-P(a-b)+W(b+c)]/[2(b+c)]y,x0(5):f1=subs(f,x,x0);%x0f2=subs(f1,{L,P,W,a,b,c},{2000,4,3,1000,1000,4000})%L,P,W,a,b,cx1=subs(x0,{L,P,W,a,b,c},{2000,4,3,1000,1000,4000})y=3.9-0.13.4;%yx=17/10+1/23y%(4)f3=(-13/10+1/23y).3(-6500+25003y)%(4)plot(y,f3)%(4)xlabel()ylabel()08()234Tab.4theoptimumsalepriceanditsprofitsofsecondgasstationy3.93.83.73.63.53.4x3.653.603.553.503.453.40f2112.51800.01512.51250.01012.5800.0(4-3)2000=2000,44,4Fig.4Theprofitsofsecondgasstation,Matlab,FORTRANC,,,,,Matlab,Matlab,,,,,,4,,,,,FORTRANC,,Mat2lab,,Matlab:(1),;(2),;(3);(4)Matlab,Matlab,,,:[1].()[M].:,1993.[2].Matlab6.0[M].:,2001.[3],.[M].:,1993.[4],.[M].:,1997.181,:Matlab