1-) A scalar function changes in a region according to equation: f (r,0,z) = Ar"z – Brz" – Cz 2-2 z-5 a)Write your scalar function: Substitute the values A, B, C, m, n and write your scalar function. Take the values from the file, "values of A_B_C_m_n_ for each student.pdf" If you skip (a) and continue to solve problem without substituting the values, your solution WILL NOT be acсepted!! z axis R=3 b) Find the gradient of your scalar function in terms of r and z c) Find the divergence of the gradient of your scalar function in terms of r and z d) Using the cylindrical closed surface given in the figure, show that the gradient of your scalar function satisfies the divergence theorem.
1-) A scalar function changes in a region according to equation: f (r,0,z) = Ar"z – Brz" – Cz 2-2 z-5 a)Write your scalar function: Substitute the values A, B, C, m, n and write your scalar function. Take the values from the file, "values of A_B_C_m_n_ for each student.pdf" If you skip (a) and continue to solve problem without substituting the values, your solution WILL NOT be acсepted!! z axis R=3 b) Find the gradient of your scalar function in terms of r and z c) Find the divergence of the gradient of your scalar function in terms of r and z d) Using the cylindrical closed surface given in the figure, show that the gradient of your scalar function satisfies the divergence theorem.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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a=4 b=3 c=6 m=5 n=2
Transcribed Image Text:1-) A scalar function changes in a region according to equation:
f (r,0,z) = Ar"z – Brz" – Cz
2-2
z-5
a)Write your scalar function:
Substitute the values A, B, C, m, n and write your scalar function.
Take the values from the file, "values of A_B_C_m_n_ for each
student.pdf" If you skip (a) and continue to solve problem
without substituting the values, your solution WILL NOT be
аcсepted!!
z axis
R=3
b) Find the gradient of your scalar function in terms of r and z
c) Find the divergence of the gradient of your scalar function in
terms of r and z
d) Using the cylindrical closed surface given in the figure, show
that the gradient of your scalar function satisfies the divergence
theorem.
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