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

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