Purchase Solution

Laplacian of a function under different coordinates

Not what you're looking for?

Ask Custom Question

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 as your answer from (a).
(c) For this section take u(x,y,z) =x ^2, Convert the formula for u into a formula for u involving spherical polar coordinates. Then compute the Laplacian using the spherical polar form. Check that your answer is 2.

Attachments
Purchase this Solution

Solution Summary

The solution shows detailed calculation of Laplacian in three different 3D coordinate systems: Cartesian (rectangular), cylindrical polar, and spherical.

Purchase this Solution


Free BrainMass Quizzes
Probability Quiz

Some questions on probability

Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.