See how Stokes' theorem is used in practice.
Log in Reuven Abramovich 8 years agoPosted 8 years ago. Direct link to Reuven Abramovich's post “In the second example G t...” In the second example G turns out to be 1/3(z^3,x^3,y^3), but then it's changed to 1/3(y^3,z^3,x^3). Is that a mistake? • (7 votes) avivbrest 8 years agoPosted 8 years ago. Direct link to avivbrest's post “Yes, it appears to be a m...” Yes, it appears to be a mistake. The wrong vector G is used for the remainder of the problem. Using the correct vector, I got a final result of positive 4/3. (5 votes) Bohn Liu 6 years agoPosted 6 years ago. Direct link to Bohn Liu's post “In the second example, se...” In the second example, second to last question, the unit normal vector’s direction is negative x-axis(because air going to outside counts positively). so when we are standing on the positive x-axis, the C’s orientation should be clockwise. alek aleksander 6 years agoPosted 6 years ago. Direct link to alek aleksander's post “I guess it's worth noting...” I guess it's worth noting that in the second example you could as well compute a surface integral along the 2x2 square just by knowing that there is such a vector field G that curl G = F. • (3 votes) macuserwannabe 5 years agoPosted 5 years ago. Direct link to macuserwannabe's post “in the definition of curl...” in the definition of curl, you take the gradient of F and use that in the integral for stoke's theorem, so why in these examples are we finding the 'anti-curl'? why cant we just find the curl of F? • (2 votes) zjleon2010 2 years agoPosted 2 years ago. Direct link to zjleon2010's post “In this butterfly net pro...” In this butterfly net problem, F is the result of cross-product, if we want to use the double integral to evaluate the result, we also need the normal vector expression on the net, which is not given in the example (1 vote) Tausif Ibne Iqbal 4 years agoPosted 4 years ago. Direct link to Tausif Ibne Iqbal's post “In the Butterfly net exam...” In the Butterfly net example the density of air is taken as 1 kg/m^3. How would the answer change if the density was something else? • (2 votes) philipalexander39 5 years agoPosted 5 years ago. Direct link to philipalexander39's post “Can we have an example wh...” Can we have an example where you solve a line integral using Stoke's? • (2 votes) Yevtushenko Oleksandr a year agoPosted a year ago. Direct link to Yevtushenko Oleksandr's post “In the first example, whe...” In the first example, where's the normal to the patch at each point ? We're looking for function F curl of which is V, but the normal vector is not mentioned at all, though Stoke's theorem requires it. My first though would have been to look for (curlF dot n = v), and n is not constant ! Isn't it ? It's a normal to the patch on the surface and not a normal to the plane in which contour resides. • (1 vote) Arun Veerabagu 8 years agoPosted 8 years ago. Direct link to Arun Veerabagu's post “In the second example whi...” In the second example while finding G vector from ∇×G=F we need G1, G2 and G3 (i, j and k components of G vector ) how did you write G3 =(y^3)/3 from • (1 vote) Alexander Wu 8 years agoPosted 8 years ago. Direct link to Alexander Wu's post “We did not take the integ...” We did not take the integral of both sides but just guessed a particular solution. If we assume that ∂G2/∂z = 0, then naturally G3 = (y^3)/3. (1 vote) dylanperazzo 10 months agoPosted 10 months ago. Direct link to dylanperazzo's post “I am confused. In the exa...” I am confused. In the example where we need to find the anti-curl of F, why is the i component of G (z^3/3) without a negative sign? According to this course and all other sources, the curl is the determinant of the matrix with the partial derivative operators and the vector field components. Thus, i would assume the j component of this matrix would be subtracted (by the definition of the determinant) and the i component of G would be -z^3/3. Any help would be appreciated. • (1 vote) David 8 years agoPosted 8 years ago. Direct link to David 's post “how is the gradient of G ...” how is the gradient of G equal to F in the second example? How can you make that assumption? • (0 votes) Adam Foster 8 years agoPosted 8 years ago. Direct link to Adam Foster's post “It's not the gradient but...” It's not the gradient but the curl of G that equals F in the second example. This is just done so that the flux integral fits into the definition of Stokes' theorem, so that the theorem can be used. This is a valid technique as long as an 'anti-curl' of the field in the flux integral exists. (2 votes)Want to join the conversation?
And it is rather simple:
Integrate y^2 from -1 to 1 and multiply by 2
∂G3/∂y-∂G2/∂z=y^2?
By seeing i can tell that u have integrated the eqn w r to dy
so int[(∂G3/∂y)*dy]−int[(∂G2/∂z)*dy]=integrate[(y^2)*dy]
From the above eqn how did you got G3 =(y^3)/3?
