Please assist with the attached problem.
(a) Calculate the Laplacian of function u(x,y,z) = x^3 - 3xy^2 + z^2 in 3D Cartesian coordinates.
(b) Convert the formula for u into formula for u involving cylindrical polar coordinates. Then compute the Laplacian using the cylindrical polar form. Show that your answer here is the same
Test for symmetry and then graph the polar equation
a) is the polar equation symmetric with respect to the polar axis?
b) is the polar equation symmetric with respect to the line theta=pi/2?
c) is the polar equation symmetric with respect to the pole?
For addition and condensation polymers, in general, which kind of polymer, addition, or condensation , is likely to be less polar?
Also, the less polar, the less able to adhere to water, so what are two polymers that would have virtually no tendency to adhere to water and why?
In normal phase column chromatography, which solvent has more eluting power: petroleum ether or dicloromethane? In what way is the eluting power of a solvent related to its polarity? In normal phase column chromatography, how does the principle of like dissolve like explain the affinity of a compound for the mobile phase, relati