8. Sketch the vector function: F/r2 and computer its divergence. The answer may surprise you...can you...
Sketch the vector function: 02 2 1 Compute its divergence. The answer may surprise you...can you explain it?
riffiths (Introduction to Electrodynamics (4th edition)): p. 18: Problem 1.16 Sketch the vector function and compute its divergence. The answer may surprise you...can yo
Sketch the vector function and compute its divergence. 2
Please describe the contour map and list important aspects of it, thanks! Let f(x,y) -2(xy 1) be a scalar function in R2. a) Find the vector field F(x, y) for which f(x, y) is a potential function, b) c) sketch a contour map of f (x, y) and, on the same figure, sketch F(x,y) (on R2). Comment on any important aspects of your sketch. Let f(x,y) -2(xy 1) be a scalar function in R2. a) Find the vector field F(x,...
answer asap Find the curl and the divergence of the vector field: F = 4x71 + 2xy j - 4xz k
The gradient vector field for a function f: R2 -> R is given at the left.
8) In this question, we will verify the divergence theorem on the vector field F = xyî - yzy - zx2. 210,0,1) (1.0.1) (1.1.1 (0,0,0) (0.1,0) (1,0,0) a. Calculate th. Fds, where R is the unit cube shown below. As discussed in class, you must add up the total outward flux from each face of the cube. b. Calculate W .FdV, where R is the unit cube. c. Do the results of a and b match? Should they match?
5. Let f R2 ->R2 be the function given by f(x, y) (х + у, х — у). (i) Prove that f is linear as a function from R2 to R2. (ii) Calculatee the matrix of f. (iii) Prove that f is a one-to-one function whose range is R2. Deduce that f has an inverse function and calculate it. (iv) If C is the square in R2 given by C = [0,1] x [0, 1], find the set f(C), illustrating...
Question 8 (15 marks) Consider the function f: R2 R2 given by 1 (, y)(0,0) f(r,y) (a) Consider the surface z f(x, y). (i Determine the level curves for the surface when z on the same diagram in the r-y plane. 1 and 2, Sketch the level curves (i) Determine the cross-sectional curves of the surface in the r-z plane and in the y- plane. Sketch the two cross-sectional curves (iii) Sketch the surface. (b) For the point (r, y)...
(a) Sketch the curve r(t) = (e cost, e sint) in R2 and compute its are length for 0 < t < 87. For the sketch, use of software is acceptable, but the graph should be drawn by hand and the right features should be present.] (b) The vector v makes an angle of with the positive -axis. Write the vector v in component form. Furthermore, write the equation of the line lt') passing through the origin with direction vector...