The discussion focuses on applying Stokes' Theorem to evaluate a line integral of a vector field when the variable z cannot be expressed in terms of x and y. Participants highlight the importance of identifying the normal vector and suggest that if the surface is cylindrical, Gauss's Law may be more appropriate than Stokes' Theorem. The use of LaTeX for vector notation, such as "∇" for gradient and "∇·" for divergence, is also emphasized for clarity in mathematical expressions.
PREREQUISITESStudents studying vector calculus, mathematics educators, and anyone seeking to understand the application of Stokes' Theorem in complex scenarios involving vector fields.
For your first case, I don't see a boundary line to the surface. For the second case, the surface is a cylinder, and I think they might be asking you to compute ## \int \vec{F} \cdot \, dS ##. If that is the case, you could also use Gauss law and compute ## \int \nabla \cdot \vec{F} \, d^3x ##, but certainly not Stokes theorem. (the Gauss's law version would also include in its result the integration over the endfaces of the cylinder). ## \\ ## Additional item: For vector curl use " \nabla \times " in Latex. To get Latex, put " ## " on both sides of your statement or expression. (The vector gradient is " \nabla" in Latex. The divergence is " \nabla \cdot ".)fonseh said:
fonseh said:
