Homework Answers
5) Let Φ : R2-ל -(rcos(0), r sin(θ)), 0-r-R, 0-θ disk of radius R centered at (0,0)). Compute J dx Λ dy. R2 given by Φ(r, θ) -2n (this is a 5) Let Φ : R2-ל -(rcos(0), r sin(θ)), 0-r-R, 0-θ disk...
5) Let Φ : R2-ל -(rcos(0), r sin(θ)), 0-r-R, 0-θ disk of radius R centered at (0,0)). Compute J dx Λ dy. R2 given by Φ(r, θ) -2n (this is a
5) Let Φ : R2-ל -(rcos(0), r sin(θ)), 0-r-R, 0-θ disk of radius R centered at (0,0)). Compute J dx Λ dy. R2 given by Φ(r, θ) -2n (this is a
only do problem 3c, the second picture is the answer to problem 2, the answer I...
only do problem 3c, the second picture is the answer
to problem 2, the answer I got for 3b is -1/(r^2)
The tinction V(x, y,z) Problem 3 (20 pts). Considering the function V of problem 2, (a) Show that V can be written in spherical coordinates as V(r, θ, φ-1. (10 pts) r + θ + φ (b) The gradient of a function in spherical coordinates is VV Calculate the gradient of V in spherical coordinates. (5 pts) (e) Show...
In problems 3-5 evaluate ∫?⃗∙??⃗? using Stokes’ theorem. In each case ? is oriented counterclockwise when...
In problems 3-5 evaluate ∫?⃗∙??⃗? using Stokes’ theorem. In each
case ? is oriented counterclockwise when viewed from
above.
4. F(x, y, z) = (z)i + (x2)j + (y – sin(z))k; c is the boundary of the helicoid given by Õ(r,0) =< rcos(6), rsin(0),>; Osrs 1, osos
4[10 pts]. Let f(z) = u (r,0) + iv(r,0) be analytic in a domain D c C which does not contain the ...
4[10 pts]. Let f(z) = u (r,0) + iv(r,0) be analytic in a domain D c C which does not contain the origin. Then do the following ones: (a) Show that rurr(r, θ) + rur(r, θ) + u69(r, θ) 0 for all re® E D. (b) Show that (a) is equivalent to the condition that u is harmonic in D (c) Show that the function (in|e )2-[Arg( a(z) z)]2,-π < Arg(z) < π,
4[10 pts]. Let f(z) = u (r,0)...
matlab code please 0 solutions submitted (max Unlimited) Problem2 A staircase of height h is modeled by the parametric equations: x = rcos(1) y = rsin(1) -=- trix where r=h[2 + 5 sin(1/8)]/10, n...
matlab code please
0 solutions submitted (max Unlimited) Problem2 A staircase of height h is modeled by the parametric equations: x = rcos(1) y = rsin(1) -=- trix where r=h[2 + 5 sin(1/8)]/10, n=4, and h 50m is the staircase height. Make a 3-D plot (shown) of the staircase. (Create a vector , for the domain 0 to 2π and use the pi1ot3 command.) so so nd ion Your Script em of 11% iength of vector t is 40e, use,...
Electricity and magnetism problem. if done right, step by step I'll to leave a like.
electricity and magnetism problem. if done right, step by step
I'll to leave a like.
42 Calculate the energy stored in the region R 2 m , 0 θ π , 0 φ π for a magnetic field intensity equal to 2Rsin θcos φ R-Rcos θcosở θ-R sin φφ A/m, in free space.
42 Calculate the energy stored in the region R 2 m , 0 θ π , 0 φ π for a magnetic field intensity equal to 2Rsin...
Question 4 Consider the polar coordinates change of variables: -rcos,y= rsin 0 Consider u = u(x,y)....
Question 4 Consider the polar coordinates change of variables: -rcos,y= rsin 0 Consider u = u(x,y). 1. Compute and 2. Pind the general and particular solution to the PDE: Tu, + yuy 2.2? + 2y?, on the domain D= {(x, y)|x+ vº > 0). with the extra condition u(x, y) y on the curve rº + y2 + 1.
(14 points) Let F be the radial vector field Ft(z, y, z) =zi+w+sk And S be the surface of the cone shown at right parameterized by G(r,)-(rcos(0),r sin(0),6-3r) Write the integral F dS using an outwa...
(14 points) Let F be the radial vector field Ft(z, y, z) =zi+w+sk And S be the surface of the cone shown at right parameterized by G(r,)-(rcos(0),r sin(0),6-3r) Write the integral F dS using an outward pointing normal in dS terms r and θ. This cone has an open bottom. . The integrand must be fully simplified » Do not evaluate the integral
(14 points) Let F be the radial vector field Ft(z, y, z) =zi+w+sk And S be the...
The result of transforming the equation r2 = 8 rcos( 0) + 3 rsin( e) from...
The result of transforming the equation r2 = 8 rcos( 0) + 3 rsin( e) from polar to rectangular coordinates is: A. 2 2 = 8x + 3y Yx +y B. 2 X +y = 3x + 8y C. Vz? + y2 = 11 D. none of the preceding E. 2 x + y = 8x + 3y
(10 marks) In class we had a question regarding the spherical coordinate system: Given that rcos θ sin φ y-rsin0 sin o with 0 θ 2π and 0 φ π "Why don't we have 0 θ π and 0 φ 2π instead...
(10 marks) In class we had a question regarding the spherical coordinate system: Given that rcos θ sin φ y-rsin0 sin o with 0 θ 2π and 0 φ π "Why don't we have 0 θ π and 0 φ 2π instead" (a) (5 marks) Explain why this would not work b) (5 marks) If you really wanted the bounds suggested how could you make it work?
(10 marks) In class we had a question regarding the spherical coordinate system:...
5) Let Φ : R2-ל -(rcos(0), r sin(θ)), 0-r-R, 0-θ disk of radius R centered at (0,0)). Compute J dx Λ dy. R2 given by Φ(r, θ) -2n (this is a
5) Let Φ : R2-ל -(rcos(0), r sin(θ)), 0-r-R, 0-θ disk of radius R centered at (0,0)). Compute J dx Λ dy. R2 given by Φ(r, θ) -2n (this is a
only do problem 3c, the second picture is the answer
to problem 2, the answer I got for 3b is -1/(r^2)
The tinction V(x, y,z) Problem 3 (20 pts). Considering the function V of problem 2, (a) Show that V can be written in spherical coordinates as V(r, θ, φ-1. (10 pts) r + θ + φ (b) The gradient of a function in spherical coordinates is VV Calculate the gradient of V in spherical coordinates. (5 pts) (e) Show...
In problems 3-5 evaluate ∫?⃗∙??⃗? using Stokes’ theorem. In each
case ? is oriented counterclockwise when viewed from
above.
4. F(x, y, z) = (z)i + (x2)j + (y – sin(z))k; c is the boundary of the helicoid given by Õ(r,0) =< rcos(6), rsin(0),>; Osrs 1, osos
4[10 pts]. Let f(z) = u (r,0) + iv(r,0) be analytic in a domain D c C which does not contain the origin. Then do the following ones: (a) Show that rurr(r, θ) + rur(r, θ) + u69(r, θ) 0 for all re® E D. (b) Show that (a) is equivalent to the condition that u is harmonic in D (c) Show that the function (in|e )2-[Arg( a(z) z)]2,-π < Arg(z) < π,
4[10 pts]. Let f(z) = u (r,0)...
matlab code please
0 solutions submitted (max Unlimited) Problem2 A staircase of height h is modeled by the parametric equations: x = rcos(1) y = rsin(1) -=- trix where r=h[2 + 5 sin(1/8)]/10, n=4, and h 50m is the staircase height. Make a 3-D plot (shown) of the staircase. (Create a vector , for the domain 0 to 2π and use the pi1ot3 command.) so so nd ion Your Script em of 11% iength of vector t is 40e, use,...
electricity and magnetism problem. if done right, step by step
I'll to leave a like.
42 Calculate the energy stored in the region R 2 m , 0 θ π , 0 φ π for a magnetic field intensity equal to 2Rsin θcos φ R-Rcos θcosở θ-R sin φφ A/m, in free space.
42 Calculate the energy stored in the region R 2 m , 0 θ π , 0 φ π for a magnetic field intensity equal to 2Rsin...
Question 4 Consider the polar coordinates change of variables: -rcos,y= rsin 0 Consider u = u(x,y). 1. Compute and 2. Pind the general and particular solution to the PDE: Tu, + yuy 2.2? + 2y?, on the domain D= {(x, y)|x+ vº > 0). with the extra condition u(x, y) y on the curve rº + y2 + 1.
(14 points) Let F be the radial vector field Ft(z, y, z) =zi+w+sk And S be the surface of the cone shown at right parameterized by G(r,)-(rcos(0),r sin(0),6-3r) Write the integral F dS using an outward pointing normal in dS terms r and θ. This cone has an open bottom. . The integrand must be fully simplified » Do not evaluate the integral
(14 points) Let F be the radial vector field Ft(z, y, z) =zi+w+sk And S be the...
The result of transforming the equation r2 = 8 rcos( 0) + 3 rsin( e) from polar to rectangular coordinates is: A. 2 2 = 8x + 3y Yx +y B. 2 X +y = 3x + 8y C. Vz? + y2 = 11 D. none of the preceding E. 2 x + y = 8x + 3y
(10 marks) In class we had a question regarding the spherical coordinate system: Given that rcos θ sin φ y-rsin0 sin o with 0 θ 2π and 0 φ π "Why don't we have 0 θ π and 0 φ 2π instead" (a) (5 marks) Explain why this would not work b) (5 marks) If you really wanted the bounds suggested how could you make it work?
(10 marks) In class we had a question regarding the spherical coordinate system:...
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