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B.2 Stokes' Theorem a. Give Stokes' theorem, defining all quantities involved, (i) in three dimensions in its standard i
Posted: Mon May 09, 2022 1:36 pm
by answerhappygod
- B 2 Stokes Theorem A Give Stokes Theorem Defining All Quantities Involved I In Three Dimensions In Its Standard I 1 (170.15 KiB) Viewed 26 times
B.2 Stokes' Theorem a. Give Stokes' theorem, defining all quantities involved, (i) in three dimensions in its standard integral form (draw a figure), and clarify how the orientation problem is resolved. (ii) in one dimension. b. Consider the following coordinates 1 = 2= 2. 5 (22 – v2), y= uv , Derive the Laplacian 2 in these coordinates by using the formula from the course. Consider the function f = y²z and evaluate 72 f in both Cartesian and the coordi- nates defined above. = c. Consider the following vector field - +) = 0 -Y Ā= x2 + y2' x2 + y2? in Cartesian coordinates. Compute the curl of this vector field and integrate its flux through the surface bounded by the upper hemisphere S Is = 5 8 xĀ.dš. Х d. Compute the line integral Ic = S.A. di, where C is the boundary of the surface S. e. Compare the two results obtained and explain why Ic # Is (i.e. Stokes' theorem does not hold here). Describe how to amend S for Stokes' theorem to hold.