Matlab 7

Matlab 7 - >>...

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MATLAB Assignment 7 Series Solutions Exercise 7.1 >> syms x >> taylor(exp(x),x,1,0) ans = 1 >> taylor(exp(x),x,9,0) ans = 1+x+1/2*x^2+1/6*x^3+1/24*x^4+1/120*x^5+1/720*x^6+1/5040*x^7+1/40320*x^8 Exercise 7.2 (a) >> syms x a0 a1 a2 a3 a4 >> a=[a0 a1 a2 a3 a4]; >> y=sum(a.*(x).^[0:4]) y = a0+a1*x+a2*x^2+a3*x^3+a4*x^4 >> dy=diff(y); >> d2y=diff(dy); >> ode=collect(d2y-x*dy-y,x) ode = -5*a4*x^4-4*a3*x^3+(12*a4-3*a2)*x^2+(6*a3-2*a1)*x+2*a2-a0 >> initcond1=strcat(char(subs(y,x,0)),'=3') initcond1 = a0=3
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>> initcond2=strcat(char(subs(dy,x,0)),'=1') initcond2 = a1=1 >> odecoeff1eq='2*a2-a0=0';
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Unformatted text preview: >> odecoeff2eq='6*a3-2*a1=0'; >> odecoeff3eq='12*a4-3*a2=0'; >> [a0 a1 a2 a3 a4]=solve(initcond1,initcond2,odecoeff1eq,odecoeff2eq,odecoeff3eq) a0 = 3 a1 = 1 a2 = 3/2 a3 = 1/3 a4 = 3/8 >> soln=subs(y) soln = 3+x+3/2*x^2+1/3*x^3+3/8*x^4 (b) >> fplot(char(soln),[-5 5],'r--')-5-4-3-2-1 1 2 3 4 5 50 100 150 200 250 300 350 Exercise 7.3 >> syms x; >> f=formalseries(x,6,0) f = a0+a1*x+a2*x^2+a3*x^3+a4*x^4+a5*x^5+a6*x^6 >> f=sersol('d2y-x*y',x,6,[1,0]) f = 1+1/6*x^3+1/180*x^6-6-5-4-3-2-1 1 2-2-1.5-1-0.5 0.5 1 1.5 2...
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Matlab 7 - >>...

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