What are the expressions for the gradient and Laplacian in cylindrical coordinates (z,r,φ)? Simplify these expressions for functions dependent on r only.
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What are the expressions for the gradient and Laplacian in cylindrical coordinates (z,r,φ)? Simplify these expressions for functions dependent on r only.
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- Let f(x, y) = arctan(xy). Find the unit vector in the direction where the directional derivative of f at (1, 2) is maximum. What is the maximum rate of change at (1, 2)?Find the moments of inertia about the coordinate axes of a thin rectangular plate of constant density δgm/cm2 bounded by the lines x = 3 and y = 3 in the first quadrant.Calculate for the axial force in kN at member DC of the frame shown in figure 2 using Cantilever Method. Enter absolute value and use 2 decimal places in your solution.
- Calculate for the axial force in kN at member GK of the frame shown in figure 2 using Cantilever Method. Enter absolute value and use 2 decimal places in your solution.A vector is said to be conservative when it's: curl equal to zero Laplacian equal to zero divergence equal to zero gradient to zero None of theseWhat is the gradient of the following scalar function, in spherical coordinates:
- where does this concave up and down?Find the bounds in cylindrical coordinates and explain how you got them easeDetermine the flow rate of water across the net if the velocity vector field for the river is given by v and the net is described by the given equations. v =〈x − y,z + y + 4, z^2〉, net given by x^2 + z^2 ≤ 1, y = 0, oriented in the positive y-direction.