Purchase Solution

Harmonic and Analytic Function

Not what you're looking for?

Ask Custom Question

Give an example (and explain why it works) of an analytic function u on a harmonic function v such that the composite function u o v is defined but NOT harmonic.

Please see the attached file for the fully formatted problem.

Attachments
Purchase this Solution
Solution Summary

Harmonic fnctions are investigated. The solution is detailed and well presented.

Purchase this Solution
Free BrainMass Quizzes
Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

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.

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.

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

View More Free Quizzes
Related BrainMass Solutions

  • To find the analytic function f(z) = u + iv when u is given.

    + 4xy , then prove that u is a harmonic function and find the analytic function f(z) = u + iv .

  • Complex Analysis Problem (analytic and harmonic functions)

    (b) Let f(z) be analytic and non-vanishing in a domain Ω. Show that ln l f(z) l is a harmonic function in Ω.

  • Harmonic complex conjugates

    Complex Mathematics Problem GHD/CMATH-003 Complex valued function If f(z) = u + iv is analytic on a domain D, then u and v are both harmonic on D. Furthermore, if ux = vy and uy = -vx ,then v is said to be a harmonic conjugate of u.

  • Analytic Functions; Harmonic Functions; Laplace\'s Equation

    Let the function ... be analytic in a domain D that does not include the origin ... 13. ... state why the functions ... are harmonic in D and why ... is in face, a harmonic conjugate 11. ... Why must this satisfy Laplace\'s equation?

  • Harmonic Functions and Cauchy-Riemann Equations

    46352 Harmonic Functions and Cauchy-Riemann Equations 15. Determine whether or not the given function u is harmonic and, if So, in what region. If it is, find the most general conjugate function v and corresponding analytic function f (z).

  • Harmonic Function: Analyticity, Compactness and Minimum Value

    46536 Harmonic Function: Analyticity, Compactness and Minimum Value Let (attached) be a function that is analytic and not constant throughtout a bounded domain (attached) and continuous (attached) on its boundary (here domain is an open connected set

  • Cauchy-Riemann equations

    For u=x2-y2-y compute ux and uy and use the Cauchy-Riemann equations to find v. The function v is called a conjugate harmonic function for u. See the attachment, please. Cauchy-Riemann equations are assessed.

  • Derivation of Poisson Integral Formula for the Half-Plane

    126845 Derivation of Poisson Integral Formula for the Half-Plane If is analytic in a domain containing the x-axis and the upper half-plane and in this domain, then the values of the harmonic function in the upper half-plane are given in terms of

  • Analyticity

    31069 Analyticity Disk Function Suppose f is analytic on the disk |z|<1 and that f(0)=0. Let g(z)=f(z)/z. Then g is analytic on the region 0<|z|<1. How can you define g(0) to make g an analytic function on all of |z|<1?

View More Related Solutions