We need at least 10 more requests to produce the answer.
0 / 10 have requested this problem solution
The more requests, the faster the answer.
Exercise 4 (15 points) (a) Calculate endz where C is a close simple counter-clockwise curve shown...
Problem 4. (5 points) Suppose f is analytic on and inside a simple closed curve C. Assume f(x) = 0 for z on C. Show f(2)=0 for all z inside C.
3. Evaluate |F.dr w tine integral is independent of path. Compute F-dr and C is the ellipse given with the counter clockwise rotation Answer by 7-6--4 4 Evaluate vf-dr where (x.y)-d C is the curve shown below. Answer. |vf.dr=-4
3. Evaluate |F.dr w tine integral is independent of path. Compute F-dr and C is the ellipse given with the counter clockwise rotation Answer by 7-6--4 4 Evaluate vf-dr where (x.y)-d C is the curve shown below. Answer. |vf.dr=-4
Please help with these need working not matlab, thanks.
2 y2 = 1 that is in the 1st quadrant with the counter clockwise 4. C is the portion of ellipse 4 rotation. (a) Express the curve C' in the form of r = x(t)i+y(t)j by using polar coordinate and specify the t value at the starting and the ending points. A2 =2 marks F.dr. where F is the vector function F = (x+y)i+(1-x)j. (b) Evaluate the line integral L =...
7. Use Green's Theorem to find Jc F.nds, where C is the boundary of the region bounded by y = 4-x2 and y = 0, oriented counter-clockwise and F(x,y) = (y,-3z). what about if F(r, y) (2,3)? x2 + y2 that lies inside x2 + y2-1. Find the surface area of this 8. Consider the part of z surface. 9. Use Green's Theorem to find Find J F Tds, where F(x, y) (ry,e"), and C consists of the line segment...
need 1-5
Midterm #3, Math 228 Each question is worth five points. 1. Let F(r.yzy). Let C be any curve that goes from A(-1,3,9) to B(1,6,-4). a) Show that F is conservative. b) Find a function φ such that ▽φ = F c) Use the result of b) to find Ic F Tds 2. Let F(z, y)-(2), and let C be the boundary of the square with vertices (1, 1). (-1,1). (-1,-1 traced out in the counter-clockwise direction. Find Jc...
Consider the vector field F2(x, y)-(-y,z) and the closed curve C which is the square with corners (-1,-1), (1,-1), (1,1), and (-1,1) and is traversed counter-clockwise starting at (-1,-1) (a) Compute the outward flux across the curve C by calculating a line integral. (b) Use an appropriate version of Green's Theorem to compute the above flux as a (c) Compute the circulation of the vector field around the curve by computing a line (d) Use an appropriate version of Green's...
1. (2 points) Find F dF if curl(F) 3 in the region defined by the 4 curves and C4 Ci F . d7 where F(x,y,z)-Wi +pz? + Vi> and C consists of the arc of the 2. (2 points) Evaluate curve y = sin(x) from (0,0) to (π, 0) and the line segment from (π,0) to (0,0). 4 3 3. (2 points) Evaluate F di where F.y,(ry, 2:,3) and C is the curve of intersection of 5 and y29. going...
QB(27pts)(a). Evaluate the circulation ofF(xy)-<x,y+x> on the curve r(t)=<2cost, 2sinp, foross2n (b) Evaluate J F.dr, where C is a piecewise smooth path from (1,0) to (2,1) and F- (e'cos x)i +(e'sinx)j [Hint: Test F for conservative (c). Use green theorem to express the line integral as a double integral and then evaluate. where C is the circle x+y-4 with counterclockwise orientation. (d(Bonus10 pts) Consider the vector field Foxyz) a. Find curl F y, ,z> F.dr where C is the curve...
7. Let f:D + C be a complex variable function, write f(x) = u(x, y) +iv(x,y) where z = x +iy. (a) (9 points) (1) Present an equivalent characterization(with u and v involved) for f being analytic on D. (Just write down the theorem, you don't need to prove it.) (2) Let f(z) = (4.x2 + 5x – 4y2 + 3) +i(8xy + 5y – 1). Show that f is an entrie function. (3) For the same f as above,...
15-4. As shown in Fig. 15.2, the density of occupied states in the conduction band goes through a maximum slightly above the bottom of the band. Calculate the energy separation (in eV) between the position of this maximum and the bottom of the band at T 300 K. You may assume that the density of states is of the form shown in equation (15.1) Ex Z(E) F(E) F(E) Z(E) Figure 15.2. Density of available states Z(E), Fermi function F(E), and...