batalla
( x , y ) → z = f ( x, y )
!
"
#
z=
1
1 + x2 + y 2
z=f(x,y)
y
x
!
$
$
$
$
x =
y =
f =
for
D = [0, 1] × [0, 2]
0 : 0.1 : 1;
0 : 0.1 : 2;inline('1/(1 + x^2 + y^2)')
j = 1:11
for i = 1:21
z(i,j) = f(x(j), y(i));
end
end
$ mesh(x,y,z), view(125,30)
$ [X, Y] = meshgrid(x, y);
$ Z = 1./(1 + X.^2 + Y.^2);
%
$ mesh(X, Y, Z)
$surf(X, Y, Z)
$ pcolor(X, Y, Z)
$ axis equal
2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
0
0.5
1
"
&
'
$ contour(X,Y,Z)
1
"
$ contour3(X,Y,Z)
0.8
0.6
0.4
0.2
0$ surfc(X,Y,Z)
0
0.5
0.5
1
1
1.5
1.5
2
2
"
#
"
(
)
z = x2 + y 2
"
#
*
+
1
)
z = x2 − y 2
",
# & '
#
0.5
0
-0.5
-1
1
0.5
1
0.50
-0.5
y
-1
0
-0.5
-1
x
"
#
-
+
1
)
z = xy
0.5
0
-0.5
-1
1
0.5
1
0.5
0
-0.5
y
-1
0
-0.5
-1
x
"
#
.
/
z = x2 + y2
0
z= 2+ x
"
#
"
z = x2 + y2
z = 3+ x / 4
1
"
#
2
3
2
z= x +y
2
2
1
0
-1
-2
y =1
2
1
1
0
0
y
-1
-1
-2
x
"
#
4
5
1
0.5
0-0.5
-1
1
0.5
x( x − y )
si ( x, y ) ≠ (0,0)
2
2 y =1
z= x +y
2
2
0
si ( x, y ) = (0,0)
1
0.5
0
-0.5
y
-1
0
-0.5
-1
x
"
#
6
"
15
,
10
5V=
q
4πε 0 r
0
1
0.5
1
0.5
0
-0.5
-1
r = x2 + y 2
-0.5
-1
0
"
#
7
z = atan( y / x)
4
2
8 ) 0
atan2(Y,X)
0
-2
-4
1
1
0.5
0.5
0
0
#NaN
-0.5
y
-0.5
-1
-1
x
*
!
"
#
$ quiver
F : D ⊂ IR 2 → IR 2
( x, y ) → (u, v)
( x, y ) → ( − y , x )
*
$ x = -1 : 0.1 : 1;
$ y = x;
1
0.8
0.6
0.4
$ [X,Y] = ...
meshgrid(x, y);
$ U = -Y;
$ V = X;
0.2
0
-0.2
-0.4
-0.6
-0.8
-1
-1
-0.5
0
0.5
1
$ quiver(X, Y, U, V)
$ quiver(X, Y, U, V, 0)
% sin autoescala
"
#
)...
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