(b) Verify that the following function is harmonic u(x, y) = -ey sin x - 2e siny. Find a harmonic conjugate v of u, namely a function v such that the function u(x,y)+iv(x,y) an analytic function, such that v(0, 0) = 4. Justify all of your steps.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.6: Additional Trigonometric Graphs
Problem 77E
icon
Related questions
Question

Hi, can i have a written solution to this questions please. Thanks!

(b) Verify that the following function is harmonic
u(x, y) = −e sin x - 2e siny.
Find a harmonic conjugate v of u, namely a function v such that the function
u(x, y) + iv(x, y) is an analytic function, such that v(0,0) = 4. Justify all of
your steps.
Transcribed Image Text:(b) Verify that the following function is harmonic u(x, y) = −e sin x - 2e siny. Find a harmonic conjugate v of u, namely a function v such that the function u(x, y) + iv(x, y) is an analytic function, such that v(0,0) = 4. Justify all of your steps.
Expert Solution
steps

Step by step

Solved in 3 steps with 3 images

Blurred answer
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning