Let z₀ = a + ic, z₁ = b + id, z₂ = -id, and z = [z₀ + z₁]. Let z₀ be the apex of the wedge with one ray passing through z₁ and the other passing through z₂, and with z in its interior. Suppose φ is a harmonic function in the wedge that contains z, z₁, z₂, and z₀, taking the value -0.5 on the ray passing through z₁ and the value 1.5 on the ray passing through z₂. What, to 3 decimal places, is the value of φ at z?

(Hint: if you can't figure out how to get the right quadrants for your angles, try breaking them into pieces - referencing each piece separately to the nearest axis, +y or -y or -x - so that each piece is between 0 and 90 degrees; then sum them up.)

Posted Date: 4/26/2013 1:52:40 AM | Location : United States

Ask an Expert

Related Discussions:- Harmonic function, Assignment Help, Ask Question on Harmonic function, Get Answer, Expert's Help, Harmonic function Discussions

Write discussion on Harmonic function
Your posts are moderated

Write your message here..

Related Questions

TRIGONOMETRY, WHY IS SINp = 0 WHY IS SINp = 0

Profit per unit , A company's full profit per unit production is given by t... A company's full profit per unit production is given by the function y = -5x 2 +17x-12  where x is the number of items produced (in hundreds) and the y is the profit per unit (in

Find the sum of the three coefficient polynomials, Find the quadratic that ... Find the quadratic that interpolates f(x) = 2x 3 - x + 1 at the nodes x 0 = 0, x 1 = 2, x 2 = 3, a) by solving a set of three equations for the coefficients of p 2 (x) = a 2

Define a mapping from the x-y plane, Define a mapping from the x,y plane to... Define a mapping from the x,y plane to the u,v plane by u = 2x + y, v = -x +2y . If a temperature function is given in the x,y plane by T(x,y) = x+y, what is the value, to 3 de

Z transform, a^n * n *u[n-1] a^n * n *u[n-1]

Partial Differentiation, if the sides of a triangle ABC vary in such a way ... if the sides of a triangle ABC vary in such a way that it''s circum-radius remains constant. prove that, da/cos A+db/cos B+dc/cos C =0

Diffrential equations homogenius, y''=2xy/x^2-y^2 y''=2xy/x^2-y^2

Investigate the output of advertising agencies, In an article in Marketing... In an article in Marketing Science , Silk and Berndt investigate the output of advertising agencies. They describe ad agency output by finding the shares of dollar billing volume

Monthly payment, Ah Fong borrow RM10 000. The yearly simple interest rate i... Ah Fong borrow RM10 000. The yearly simple interest rate is 10.5%, payable monthly, and the monthly payment is RM200. How much of the 1st payment goes to interest and how much to p

Find the polynomial, a) Use divided differences to ?nd the polynomial (in n... a) Use divided differences to ?nd the polynomial (in nested form) that interpolates the data b) Add the data point x = 6, y = -20 and hence estimate y for x = 2.