15.4. Green’s Theorem
Ex. 1
1/6 1/6 |
1/5 1/5 |
-1/30 -1/30 |
0 0 |
1/6 1/6 |
Ex. 2
36*pi 36*pi |
Ex. 3
pi*a*b pi*a*b |
Ex. 4
14/3 14/3 |
Ex. 5
0 0 |
2*pi 2*pi |
Exercise 1
![]() |
7*pi 7*pi |
![]() |
7*pi 7*pi |
Exercise 2
![]() |
dQ/dx-dP/dy = 1/(x^2 + 1) 1/4*pi - 1/2*log(2) dQ/dx-dP/dy = 1/(x^2 + 1) 1/4*pi - 1/2*log(2) |
1/4*pi + 1/2*sqrt(2) + 1/2*arcsinh(1) - 1/2*log(2) 1/4*pi + 1/2*sqrt(2) + 1/2*arcsinh(1) - 1/2*log(2) |
-1/2*sqrt(2) - 1/2*arcsinh(1) -1/2*sqrt(2) - 1/2*arcsinh(1) |
0 0 |
1/4*pi - 1/2*log(2) 1/4*pi - 1/2*log(2) |
15.5. Curl and Divergence
Ex. 1
(-x*y - 2*y, x, y*z) (-x*y - 2*y, x, y*z) |
Ex. 3
(0, 0, 0) (0, 0, 0) |
Ex. 4
x*z + z x*z + z |
Exercise 1
curl F = (-x*y^2 + x*z^2, x^2*y - y*z^2, -x^2*z + y^2*z) div F = 6*x*y*z curl F = (-x*y^2 + x*z^2, x^2*y - y*z^2, -x^2*z + y^2*z) div F = 6*x*y*z |
Exercise 2
curl F = (0, 0, 0) curl F = (0, 0, 0) |
fx = e^x*sin(y*z) fy = z*cos(y*z)*e^x fz = y*cos(y*z)*e^x fx = e^x*sin(y*z) fy = z*cos(y*z)*e^x fz = y*cos(y*z)*e^x |
e^x*sin(y*z) z*cos(y*z)*e^x y*cos(y*z)*e^x e^x*sin(y*z) z*cos(y*z)*e^x y*cos(y*z)*e^x |
|