Question

harmonic conjugate of u(x,y)= e^y cosx​

Answer 1

Answer:

For u(x,y)=e−ysinxu(x,y)=e−ysin⁡x, we have u,1(x,y)=∂u(x,y)∂x=e−ycosxu,1(x,y)=∂u(x,y)∂x=e−ycos⁡x and u,2(x,y)=∂u(x,y)∂y=−e−ysinxu,2(x,y)=∂u(x,y)∂y=−e−ysin⁡x. Hence taking the straight-line path γ:τ∈[0,1]↦(xτ,yτ)γ:τ∈[0,1]↦(xτ,yτ) joining (0,0)(0,0) to (x,y)(x,y), we have

∫(x

Step-by-step explanation:

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