일반수학및실습2-11.6절

2166 days 전, jhlee2chn 작성

예제 1.

var('t') f(t)=t*cos(t);g(t)=t*sin(t);h(t)=t r(t)=[f(t), g(t), h(t)] print diff(r(t), t).subs(t=pi) 
       
(-1, -pi, 1)
(-1, -pi, 1)

예.

var('t') f(t)=t^2+t;g(t)=exp(t);h(t)=2 r(t)=[f(t), g(t), h(t)] dr=diff(r, t);d2r=diff(dr, t) print "r'(t)=", dr(t) print "r''(t)=", d2r(t) 
       
r'(t)= (2*t + 1, e^t, 0)
r''(t)= (2, e^t, 0)
r'(t)= (2*t + 1, e^t, 0)
r''(t)= (2, e^t, 0)
ip=dr(0).inner_product(d2r(0)) drn=dr(0).norm();d2rn=d2r(0).norm() (arccos(ip/(drn*d2rn))*180/pi).n(digits=4) 
       
18.44
18.44

예.

var('t') f(t)=t^2;g(t)=exp(-t);h(t)=-2 F(t)=[f(t), g(t), h(t)] print diff(t^3*F(t), t) print integral(F(t), t, 0, 1) 
       
(5*t^4, -t^3*e^(-t) + 3*t^2*e^(-t), -6*t^2)
(1/3, -e^(-1) + 1, -2)
(5*t^4, -t^3*e^(-t) + 3*t^2*e^(-t), -6*t^2)
(1/3, -e^(-1) + 1, -2)