MATLAB 기호프로세서(symbolic processor) 기초2
1. 연립방정식
solve(eq1,eq2,… ,eqn,var1,var2,…,varn)
>> S = sym('x^2+3*x+18');
>> solve(S)
ans =
- 3/2 - (3*7^(1/2)*i)/2
- 3/2 + (3*7^(1/2)*i)/2
>> pretty(solve(S))
>> eq1 = '3*x+2*y-z-10'
>> eq2 = '-x+3*y+2*z-5'
>> eq3 = 'x-y-z+1'
>> answer = solve(eq1,eq2,eq3)
answer =
x: [1x1 sym]
y: [1x1 sym]
z: [1x1 sym]
>> answer.x
ans =
-2
>> answer.y
ans =
5
>> answer.z
ans =
-6
2. 미분, 적분
diff(f,'t',n)
symbolic으로 표현된 f를 t에 관하여 n번 미분
>> syms x y z
>> f1 = 6*x^3-4*x^2+y^3-8*y^2-5;
>> f2 = sin(x);
>> f3 = (1-z^3)/(1+z^4);
>> diff(f1)
ans =
18*x^2 - 8*x
>> diff(f1,2)
ans =
36*x - 8
>> diff(f1,y,2)
ans =
6*y - 16
>> diff(f2,5)
ans =
cos(x)
>> diff(f3)
ans =
(4*z^3*(z^3 - 1))/(z^4 + 1)^2 - (3*z^2)/(z^4 + 1)
>> pretty(diff(f3))
int(f,'t',a,b)
symbolic으로 표현된 f를 t에 관하여 a에서 b까지 적분
>> f1 = 6*x^2-5*x+5;
>> int(f1)
ans =
(x*(4*x^2 - 5*x + 10))/2
>> int(f1,1,2)
ans =
23/2
>> int(f1,'a','b')
ans =
- 2*a^3 + (5*a^2)/2 - 5*a + 2*b^3 - (5*b^2)/2 + 5*b
>> int(f1,'y')
ans =
y*(6*x^2 - 5*x + 5)
3. 미분방정식
dsolve(eq1,eq2,…,'boundary or initial condition','var')
>> dsolve('Dx = -a*x')
ans =
C2/exp(a*t)
>> dsolve('Dx = -a*x','x(0)=1')
ans =
1/exp(a*t)
>> S = dsolve('Df = f + g','Dg = -f + g','f(0) = 1','g(0) = 2')
S =
f: [1x1 sym]
g: [1x1 sym]
>> S.f
ans =
exp(t)*cos(t) + 2*exp(t)*sin(t)
>> S.g
ans =
2*exp(t)*cos(t) - exp(t)*sin(t)