In summary, the conversation discusses the evaluation of a surface integral using the divergence theorem and Stokes' theorem. While the divergence theorem gives a dot product and the Stokes' theorem gives a cross product, both methods result in a value of 0 for this particular prob...
because I had a lot of Ph.D students. I really believe the battle in graduate school is the hardest time, hardest time for research for me, I don’t know if it was like this for you. Because I knew the least of mathematics, but I am supposed to prove the theorem, now you...
To be frank, especially if you aren't exactly up on your vector calculus, Maxwell's equations look quite daunting despite how relatively compact they all are. The best way to really understand them is to go through some examples of using them in practice, and Gauss' law is the best pl...
In between the two limiting cases, the surface {\hat{y}=\hat{y}\left( t,\beta \right) } can be proven to be increasing in \beta , since by the implicit function theorem, we have \begin{aligned} f(t,\beta ,\hat{y})&=\sum _{n=0}^{\infty }\frac{\hat{y}^{\beta n+1}...
Gradient theorem:Works with multidimensional curves; relates an integral over the interior of a region to an integral over the region’sboundary. Green’s Theorem:The fundamental theorem applied to planes. Stokes’ Theorem:Relates the derivative and the boundary to surfaces in three dimensions. ...
How do you calculate the cross product for curl? Cross Product of Vectors: The result of the cross product of two vectors is a third vector perpendicular to the two initial vectors. It gives the size of the parallelogram between them and the right thumb rule can determine its orientation. ...
Convert Maxwell's equations from integral to differential form using Stokes's and the divergence theorem. Explain the major contribution of Maxwell in correcting Ampere's circuital law. Write the mathematical relationship for this. Maxwell's equations proved that a. Light is a...
, or which could be trivially adapted to cover the case). While global errors are less constructive than local errors, and thus less satisfying as a “smoking gun”, they tend to be significantly more robust. A local error can often be patched or worked around, espe...
Stokes’ theory this viscous flow of ether would fall off at a very rapid rate as we recede from the surface of separation. Michelson and Morley repeated their experiment at different heights from the surface of the earth, but invariably obtained the same negative results, thus failing to ...
Explain the work energy theorem. Briefly describe the phenomenon of magnetization. What is a magnetic dipole? How is its strength defined? Answer the following question. What is Dalton's law of partial pressure? Explain Stokes' law and how it can be applied....