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4.1 In aerodynamics and fluid mechanics, the functions u(x,y) and v(x,y) in f(z) = u(x,y) + iv(x,y), where f(z) is analytic, are called the velocity potential and stream function, respectively. If the function u(x,y) = e2* sin(2y) + 9bxy2 - x³, find a) the value of b that satisfy u(x,y) to be a harmonic function, and

4.1 In aerodynamics and fluid mechanics, the functions u(x,y) and v(x,y) in f(z) = u(x,y) + iv(x,y), where f(z) is analytic, are called the velocity potential and stream function, respectively. If the function u(x,y) = e2* sin(2y) + 9bxy2 - x³, find a) the value of b that satisfy u(x,y) to be a harmonic function, and

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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4.1 In aerodynamics and fluid mechanics, the functions u(x, y) and v(x, y) in f(z) where f(z) is analytic, are called the velocity potential and stream function, respectively. u(x, y) = e2* sin(2y) + 9bxy? – x³, find a) the value of b that satisfy u(x,y) to be a harmonic function, and b) the value of f(=) at z = 2- i. u(x, y) + i v(x,y), If the function %3D
Transcribed Image Text:4.1 In aerodynamics and fluid mechanics, the functions u(x, y) and v(x, y) in f(z) where f(z) is analytic, are called the velocity potential and stream function, respectively. u(x, y) = e2* sin(2y) + 9bxy? – x³, find a) the value of b that satisfy u(x,y) to be a harmonic function, and b) the value of f(=) at z = 2- i. u(x, y) + i v(x,y), If the function %3D
5.1 Solve the following integral. a) -dx x3 b) =dx x(3-x)
Transcribed Image Text:5.1 Solve the following integral. a) -dx x3 b) =dx x(3-x)
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