2. Verify that each given function u is harmonic (in the region where it is defined), then find a harmonic conjugate of u and the analytic function f(z) whose real part is u: (a) u = y u = e sin y u = xy = x + y

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A: Use Hessian matrix

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A:

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A: Given:To find:value of f(S,v) when S=103.5

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A:

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A: This is a problem of multivariable Calculus.

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A: Given:  The equation: x3 + 3y2 + 4xz2 - 3z2y = 1. To define: z in the equation as a function of x…

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A:

Q: tch the following contour diagrams (cross-sections to the z-axis) to the following fund II) IV) 0.5…

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A:

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Q: implicitly by the equation y tan-1(xz) − x cos(yz) = 3. Find zy.

A:

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A: Continuous function

Q: Draw the level curve for z = f(x, y) for each of the values listed below. Label each level curve…

A: Equating 2x2-y = z Equating with the values of z we can draw the graph for each function