If z= 3r+5t+7y, what is dz/dt and dz/dy
Apply Stokes' theorem to evaluate the integral ∫C (5x^2y^2 - 8yz^2)dx + (3x^3y - 4xz^2)dy - 5xyzdz; where C is the curve of intersection of the surface z = x^2 +y^2 with the plane z = 3 + x + y.
Use the Divergence Theorem to calculate the surface integral F · dS, that is, calculate the flux of F across S.
S is the surface of the solid bounded by the cylinder
Use Green's Theorem to evaluate the line integral
where is triangle with vertices and oriented counterclockwise.
Use Green's Theorem in the form of this equation to prove Green's first identity, where D and C satisfy the hypothesis of Green's Theorem and the appropriate partial derivatives of f and g exist and are continuous. (The quantity grad