2.3.3.4. Содержание отчета
Название лабораторной работы.
Индивидуальное задание.
Протокол вычислений в командном окне Command Window.
2.3.3.5. Пример выполнения задания
>> syms k a x >> subs(sin(k*x+1),k,a*x.^2) ans = sin(a*x^3+1)
>> x=2 x = 2 >> sin(a*x^3+1) >> simplify(ans) ans = sin(a*x^3+1)
>> taylor(ans) ans = sin(1)+cos(1)*a*x^3
>> taylor(int(ans)) ans = sin(1)*x+1/4*cos(1)*a*x^4
>> v=sym('x') >> v=(x+1)^2 v = (x+1)^2 >> factor((x+1)^2) ans = (x+1)^2
>> sym z ans = z >> d=(z+1)^2 d = Columns 1 through 6 11445 8946 7161 6090 5733 6090 7623 6006 4851 4158 3927 4158 4893 3906 3201 2778 2637 2778 3255 2646 2211 1950 1863 1950 2709 2226 1881 1674 1605 1674 3255 2646 2211 1950 1863 1950 4893 3906 3201 2778 2637 2778 7623 6006 4851 4158 3927 4158 11445 8946 7161 6090 5733 6090 Columns 7 through 9 7161 8946 11445 4851 6006 7623 3201 3906 4893 2211 2646 3255 1881 2226 2709 2211 2646 3255 3201 3906 4893 4851 6006 7623 7161 8946 11445
>> z=sym('z') >> factor((z+1)^2) ans = (z+1)^2
>> x=2; >> symsum((1+x)^i,i,0,3) >> i=sym('i'); >> symsum((1+x)^i,i,0,3) ans = 40
>> diff((cos(z-1)+z)/z.^2,z) ans = (-sin(z-1)+1)/z^2-2*(cos(z-1)+z)/z^3
>> simplify(ans) ans = -(z*sin(z-1)+z+2*cos(z-1))/z^3
>> int((cos(z-1)+z)/z.^2,z) ans = -cos(z-1)/z-sinint(z)*cos(1)+cosint(z)*sin(1)+log(z)
>> simplify(ans) ans = -(cos(z-1)+sinint(z)*cos(1)*z-cosint(z)*sin(1)*z-log(z)*z)/z
>> z=3 z = 3 >> diff((cos(z-1)+z)/z.^2,z) ans = []
>> z=sym('z') z = z >> int((cos(z-1)+z)/z.^2,z) ans = -cos(z-1)/z-sinint(z)*cos(1)+cosint(z)*sin(1)+log(z)
>> int((cos(z-1)+z)/z.^2,z,1,4) ans = 1-cosint(1)*sin(1)+sinint(1)*cos(1)-1/4*cos(3)+2*log(2)+cosint(4)*sin(1)-sinint(4)*cos(1)
>> int((cos(z-1)+z)/z.^2,z,1,2) ans = 1-cosint(1)*sin(1)+sinint(1)*cos(1)-1/2*cos(1)+log(2)+cosint(2)*sin(1)-sinint(2)*cos(1)
>> limit((cos(z-1)+z)/z.^2) ans = Inf
>> limit((cos(z-1))/z.^2) ans = Inf
>> limit((cos(z-1)+z)/z.^2,pi/2) ans = (4*sin(1)+2*pi)/pi^2
>> prod((1+z)^i,i) ans = (1+z)^i >> z=2;
>> prod((1+z)^i,i) ans = 3^i >> t=2 t = 2 >> prod((1+t)^i) ans = 3^i
>> [t]=0:1:3 t = 0 1 2 3 >> w=2 w = 2 >> [i]=0:1:3 i = 0 1 2 3 >> [e]=(1+w).^i e = 1 3 9 27 >> prod(e) ans = 729
>> syms k a x >> subs(sin(k*x+1),k,a*x.^2) ans = sin(a*x^3+1) >>
>> syms k a x >> subs(sin(k*x+1),k,a*x.^2) ans = sin(a*x^3+1)
>> x=2 x = 2 >> ans ans = sin(a*x^3+1) >> ans ans = sin(a*x^3+1) >> sin(a*x^3+1) ans = sin(8*a+1) >> taylor(ans) ans = sin(1)+8*cos(1)*a-32*sin(1)*a^2-256/3*cos(1)*a^3+512/3*sin(1)*a^4+4096/15*cos(1)*a^5 >> pretty(ans)
2 3 4 sin(1) + 8 cos(1) a - 32 sin(1) a - 256/3 cos(1) a + 512/3 sin(1) a
4096 5 + ---- cos(1) a 15
>> f3= @(x) (x+1)^2 f3 = @(x)(x+1)^2 >> f3 = sym((x+1)^2) f3 = 9
>> sym z ans = z >> f3=sym('(z+1)^2') f3 = (z+1)^2 >> collect(f3) ans = 1+z^2+2*z
>> collect(f3,'z') ans = 1+z^2+2*z
>> expand(f3) ans = 1+z^2+2*z
>> sym y ans = y >> f4=sym('(cos(y-1)+y)/y^2') f4 = (cos(y-1)+y)/y^2 >> collect(f4) ans = 1/y+cos(y-1)/y^2
>> expand(f3) ans = 1+z^2+2*z
>> collect(f3,'y') ans = (z+1)^2
>> collect(f4,'y') ans = 1/y+cos(y-1)/y^2
>> expand(f4) ans = 1/y^2*cos(y)*cos(1)+1/y^2*sin(y)*sin(1)+1/y
>> factor(f4) ans = (cos(y-1)+y)/y^2
>> simple(f4) simplify: (cos(y-1)+y)/y^2 radsimp: (cos(y-1)+y)/y^2
combine(trig): (cos(y-1)+y)/y^2
factor: (cos(y-1)+y)/y^2
expand: 1/y^2*cos(y)*cos(1)+1/y^2*sin(y)*sin(1)+1/y combine: (cos(y-1)+y)/y^2
convert(exp): (1/2*exp(i*(y-1))+1/2/exp(i*(y-1))+y)/y^2
convert(sincos): (cos(y-1)+y)/y^2
convert(tan): ((1-tan(1/2*y-1/2)^2)/(1+tan(1/2*y-1/2)^2)+y)/y^2
collect(y): 1/y+cos(y-1)/y^2
mwcos2sin: (cos(y-1)+y)/y^2
ans = (cos(y-1)+y)/y^2
>> simplify(f4) ans = (cos(y-1)+y)/y^2
>> limit(f4,'y', 0) ans = Inf
>> ezplot(f4) >> limit(f3,'y',10,'left') ans = (z+1)^2
>> limit(f3,'y',10,'right') ans = (z+1)^2
>> diff(f4,'y') ans = (-sin(y-1)+1)/y^2-2*(cos(y-1)+y)/y^3
>> y=3; >> (-sin(y-1)+1)/y^2-2*(cos(y-1)+y)/y^3 ans = -0.1813
>> diff(f4,'y',2) ans = -cos(y-1)/y^2-4*(-sin(y-1)+1)/y^3+6*(cos(y-1)+y)/y^4
>> int(f4,'y') ans = -cos(y-1)/y-sinint(y)*cos(1)+cosint(y)*sin(1)+log(y) >> int(f4,'y',1,4) ans = 1-cosint(1)*sin(1)+sinint(1)*cos(1)-1/4*cos(3)+2*log(2)+cosint(4)*sin(1)-sinint(4)*cos(1) >>1-cosint(1)*sin(1)+sinint(1)*cos(1)-1/4*cos(3)+2*log(2)+cosint(4)*sin(1)-sinint(4)*cos(1) ans = 1.7925 |
