![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 that the result from b) is equivalent to the solution of problem 2. (5 pts) For this problem remember that the relations betureen cartesian coordinates and spher r rcos()sin(6), ical coordinates are cos-1 ( -) 10, 2m], y rsin()sin(8).](http://img.homeworklib.com/questions/a237b9e0-70ba-11ea-ac8a-b53d2c46e28e.png?x-oss-process=image/resize,w_560)
only do problem 3c, the second picture is the answer to problem 2, the answer I got for 3b is -1/(r^2)
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only do problem 3c, the second picture is the answer
to problem 2, the answer I...
only do problem 3a,b. show full work Problem 2 (20 pts). The function V (x, y,...
only do problem 3a,b.
show full work
Problem 2 (20 pts). The function V (x, y, z) = 7.,3,2)yt Calculate v. 1,2+22 C 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) (b) The gradient of a function in spherical coordinates is ▽V = r + θ + φ 1 a Calculate the gradient of V in spherical coordinates. (5 pts)
A. Make a sketch of a vector F- (x,y, z), labeling the appropriate spherical coordinates. In addi...
A. Make a sketch of a vector F- (x,y, z), labeling the appropriate spherical coordinates. In addition, show the unit vectors r, θ, and φ at that point B. Write the vectors ŕ.0, and ф in terms of the unit vectors x, y, and г. Here's the easy way to do this 1. For r, simply use the fact that/r 2. For φ, use the following formula sin θ Explain why the above formula works 3. Compute θ via θ...
MARK WHICH OF THE FOLLOWING ARE TRUE/FALSE A. The component of flux, given flux density F,...
MARK WHICH OF THE FOLLOWING ARE TRUE/FALSE
A. The component of flux, given flux density F, crossing the surface dsu F.ûdsu OB. In spherical coordinates the following is true for any point, r= Rsin o cos 6î + Rsin o sin oſ + R cos and de =R c. The gradient in the u, v, w coordinates is 1 0 1 0 V= ü+T V .hu du h, du + 1 0 hw dw Then, the component of flux, given...
Question 2. Comsider fcn log(2 - 2) (x2 + y2) (e) Find the level set of f which has value "height...
Question 2. Comsider fcn log(2 - 2) (x2 + y2) (e) Find the level set of f which has value "height") wo 0, and describe it in words and set notation. Confirm that the point (2, 2, 1) is on this level surface, and that Vf(2,2, 1) is perpendicular to this surface. (f) Using cylindrical and spherical coordinates find feyl(p,9,2) and fsm(r, θ, φ). (g) Express the cartesian point (V3,-v3,-v/2) in cylindrical and spherical coordinates. Use your answers to directly...
2nd attached picture is problem 1 from HW 2 1. (10 Points Exam Extra Credit): Let's...
2nd attached picture is problem 1 from HW 2
1. (10 Points Exam Extra Credit): Let's revisit the problem of how to compute derivatives of basis vectors, which we did in Problem 1 of HWW2 (note: you will need to refer back to this HW at to do this problem). Consider the Laplacian operator, V2, in spherical coordinates. It looks like this, where the scalar (say V) goes into the 2) 10.2001 8801 VO - por l" or ) +...
Log(2 - 2) (x2 y Question 2. Consider the function f(x, y, (a) What is the maximal domain of f? (...
log(2 - 2) (x2 y Question 2. Consider the function f(x, y, (a) What is the maximal domain of f? (Write your answer in set notation.) (b) Find ▽f. (c) Find the tangent hyperplnes Te2)(r, y,z) and Tao2-)f(x, y, z). Find the intersection of these two hyperplanes, and very briefly describe the intersection in words (0,1, 1) and set notation. Confirm that the point (2, 2, 1) is on this level surface, and that Vf(2, 2, 1) is (d) On...
Help please. I would really appreciate clear, full explanation of the method used. like and comment are rewarded for good answer. (a) Let v(r) be a scalar function of r, where r V +y? +22 (i) Show...
Help please. I would really appreciate clear, full
explanation of the method used. like and comment are rewarded for
good answer.
(a) Let v(r) be a scalar function of r, where r V +y? +22 (i) Show that (i) If F Vu) evaluate Jc Fdr where C is straight line going from the point defined by vector r1 to the point defined by r2 (b) Consider a body with a surface defined by 2(x2 + y2) + 4z2 1 (i)...
Change of Variables When working integrals, it is wise to choose a coordinate system that fits the problem; e.g. p...
Change of Variables When working integrals, it is wise to choose a coordinate system that fits the problem; e.g. polar coordinates are a good choice for integrating over disks. Once we choose a coordinate system we must figure out the area form (dA) for that system. For example, when switching from rectangular to polar coordinates we must change the form of the area element from drdy to rdrd0. To determine that rdrde is the correct formula how the edges of...
019.09 points | Previous Answers SerCP9 1.AE.009 EXAMPLE 1.9Cartesian and Polar Coordinates GOAL Understand how to...
019.09 points | Previous Answers SerCP9 1.AE.009 EXAMPLE 1.9Cartesian and Polar Coordinates GOAL Understand how to convert from plane rectangular coordinates to plane polar coordinates and vice versa. y (m) PROBLEM (a) The Cartesian coordinates of a point in the xy-plane are (x,y) (-3.50 m, -2.50 m), as shown in the NY figure. Find the polar coordinates of this point. (b) Convert (r, θ) = (5.00 m, 37.0°) to rectangular coordinates x (m) (-3.50,-2.50) STRATEGY Apply the trigonometric functions and...
please provide the complete code for python Problem 2 (11 pts) From heat transfer, you should...
please provide the complete code for python
Problem 2 (11 pts) From heat transfer, you should recall that Fourier's law of conduction states where λ is the thermal conductivity and q is the heat flux (a vector. Recall that can be written in Cartesian coordinates as v- + is the gradient operator, which In addition, for constant λ. aT where is the thermal diffusivity and V2 is the Laplacian, which in Cartesian coordinates is ▽2 + 하륜 Recall that V...
only do problem 3a,b.
show full work
Problem 2 (20 pts). The function V (x, y, z) = 7.,3,2)yt Calculate v. 1,2+22 C 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) (b) The gradient of a function in spherical coordinates is ▽V = r + θ + φ 1 a Calculate the gradient of V in spherical coordinates. (5 pts)
A. Make a sketch of a vector F- (x,y, z), labeling the appropriate spherical coordinates. In addition, show the unit vectors r, θ, and φ at that point B. Write the vectors ŕ.0, and ф in terms of the unit vectors x, y, and г. Here's the easy way to do this 1. For r, simply use the fact that/r 2. For φ, use the following formula sin θ Explain why the above formula works 3. Compute θ via θ...
MARK WHICH OF THE FOLLOWING ARE TRUE/FALSE
A. The component of flux, given flux density F, crossing the surface dsu F.ûdsu OB. In spherical coordinates the following is true for any point, r= Rsin o cos 6î + Rsin o sin oſ + R cos and de =R c. The gradient in the u, v, w coordinates is 1 0 1 0 V= ü+T V .hu du h, du + 1 0 hw dw Then, the component of flux, given...
Question 2. Comsider fcn log(2 - 2) (x2 + y2) (e) Find the level set of f which has value "height") wo 0, and describe it in words and set notation. Confirm that the point (2, 2, 1) is on this level surface, and that Vf(2,2, 1) is perpendicular to this surface. (f) Using cylindrical and spherical coordinates find feyl(p,9,2) and fsm(r, θ, φ). (g) Express the cartesian point (V3,-v3,-v/2) in cylindrical and spherical coordinates. Use your answers to directly...
2nd attached picture is problem 1 from HW 2
1. (10 Points Exam Extra Credit): Let's revisit the problem of how to compute derivatives of basis vectors, which we did in Problem 1 of HWW2 (note: you will need to refer back to this HW at to do this problem). Consider the Laplacian operator, V2, in spherical coordinates. It looks like this, where the scalar (say V) goes into the 2) 10.2001 8801 VO - por l" or ) +...
log(2 - 2) (x2 y Question 2. Consider the function f(x, y, (a) What is the maximal domain of f? (Write your answer in set notation.) (b) Find ▽f. (c) Find the tangent hyperplnes Te2)(r, y,z) and Tao2-)f(x, y, z). Find the intersection of these two hyperplanes, and very briefly describe the intersection in words (0,1, 1) and set notation. Confirm that the point (2, 2, 1) is on this level surface, and that Vf(2, 2, 1) is (d) On...
Help please. I would really appreciate clear, full
explanation of the method used. like and comment are rewarded for
good answer.
(a) Let v(r) be a scalar function of r, where r V +y? +22 (i) Show that (i) If F Vu) evaluate Jc Fdr where C is straight line going from the point defined by vector r1 to the point defined by r2 (b) Consider a body with a surface defined by 2(x2 + y2) + 4z2 1 (i)...
Change of Variables When working integrals, it is wise to choose a coordinate system that fits the problem; e.g. polar coordinates are a good choice for integrating over disks. Once we choose a coordinate system we must figure out the area form (dA) for that system. For example, when switching from rectangular to polar coordinates we must change the form of the area element from drdy to rdrd0. To determine that rdrde is the correct formula how the edges of...
019.09 points | Previous Answers SerCP9 1.AE.009 EXAMPLE 1.9Cartesian and Polar Coordinates GOAL Understand how to convert from plane rectangular coordinates to plane polar coordinates and vice versa. y (m) PROBLEM (a) The Cartesian coordinates of a point in the xy-plane are (x,y) (-3.50 m, -2.50 m), as shown in the NY figure. Find the polar coordinates of this point. (b) Convert (r, θ) = (5.00 m, 37.0°) to rectangular coordinates x (m) (-3.50,-2.50) STRATEGY Apply the trigonometric functions and...
please provide the complete code for python
Problem 2 (11 pts) From heat transfer, you should recall that Fourier's law of conduction states where λ is the thermal conductivity and q is the heat flux (a vector. Recall that can be written in Cartesian coordinates as v- + is the gradient operator, which In addition, for constant λ. aT where is the thermal diffusivity and V2 is the Laplacian, which in Cartesian coordinates is ▽2 + 하륜 Recall that V...
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