Gradiente, Divergencia Y Rotacional

Héctor Reyes A01210837
1.- Calcular el gradiente de F
>> F=4*x*z^2+3*y*z;
>> grad1=diff(F,x)

grad1 =

24 z
>> grad2=diff(F,y)

grad2 =

3 z
>> grad3=diff(F,z)

grad3 =

8 z x + 3 y

>>grad=[grad1,grad2,grad3]

grad =

[ 2 ]
[4 z , 3 z, 8 z x + 3 y]
>>
2.- Hallar la divergencia y el rotacional de a ,b, c.
a)
>> syms x y z;
>> u=exp(x*y);
>> v=sin(x*y);
>> w=(cos(x*z))^2;
>> div= simplify(diff(u,x)+diff(v,y)+diff(w,z))

div =

y exp(y x) +cos(y x) x - 2 cos(z x) sin(z x) x
>> r1=(diff(w,y)-diff(v,z))

r1 =

0
>> r2= (diff(u,z)-diff(w,x))

r2 =2 cos(z x) sin(z x) z
>> r3=(diff(v,x)-diff(u,y))

r3 =

cos(y x) y - x exp(y x)
>> rot=[r1,r2,r3]

rot =

[0, 2 cos(z x) sin(z x)z, cos(y x) y - x exp(y x)]

b)
>> u=(x^2)*y; v=(y^2)*z; w=(-2*x*z);
>> div= simplify(diff(u,x)+diff(v,y)+diff(w,z))

div =

2 y x + 2 z y - 2 x>> r1=(diff(w,y)-diff(v,z))

r1 =

2
-y
>> r2= (diff(u,z)-diff(w,x))

r2 =2 z
>> r3=(diff(v,x)-diff(u,y))

r3 =

2
-x
>> rot=[r1,r2,r3]

rot =[ 2 2]
[-y , 2 z, -x ]
c)
>> u=(16*x*y)-z; v=(8*x^2); w=-x;
>> div= simplify(diff(u,x)+diff(v,y)+diff(w,z))

div =...