Laplace Operators and Gradient Vectors
Not what you're looking for?
Let f(z)=u+iv be an analytic function, phi(u,v) any function with second order partial derivatives and g(u,v) any function with first order partial derivatives.
a) Let L_x,y be the Laplace operator in x,y coordinates and L_u,v be the Laplace operator in u,v coordinates. Show that L_x,y(phi o f)=L_u,v |f'(z)|^2
b)Let G_u,v be the gradient vector in u,v, and G_x,y be the gradient vector in x,y coordinates. Show that |G_x,y(g o f)|^2=|G_u,v(g)|^2 |f'(z)|^2 where the | | is the euclidean norm in C.
Purchase this Solution
Solution Summary
Laplace Operators and Gradient Vectors are investigated. The solution is detailed and well presented.
Purchase this Solution
Free BrainMass Quizzes
Solving quadratic inequalities
This quiz test you on how well you are familiar with solving quadratic inequalities.
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.
Geometry - Real Life Application Problems
Understanding of how geometry applies to in real-world contexts