Explore tens of thousands of sets crafted by our community.
The Cauchy-Riemann Equations
30
Flashcards
0/30
u(x,y) = \tan^{-1}(y/x); v(x,y) = -\frac{1}{2}\ln(x^2+y^2)
Yes
u(x,y) = x^3 - 3x^2y; v(x,y) = 3x^3 + y^3
No
u(x,y) = e^{x^2-y^2}; v(x,y) = 2xe^{x^2-y^2}
No
u(x,y) = \arcsin\left(\frac{x^2-y^2}{x^2+y^2}\right); v(x,y) = \arctan\left(\frac{2xy}{x^2-y^2}\right)
No
u(x,y) = \sin(x)\cos(y); v(x,y) = \cos(x)\sin(y)
No
u(x,y) = y\exp(-x); v(x,y) = x\exp(-y)
No
u(x,y) = x^2 + y^2; v(x,y) = 2xy
No
u(x,y) = \sin(y)e^x; v(x,y) = \cos(y)e^x
Yes
u(x,y) = \frac{y}{x}; v(x,y) = \ln\left(\sqrt{x^2 + y^2}\right)
No
u(x,y) = x^2y^2; v(x,y) = (x^2 - y^2)^2
No
u(x,y) = \frac{x}{x^2 + y^2}; v(x,y) = \frac{y}{x^2 + y^2}
No
u(x,y) = \exp(-x)\cos(y); v(x,y) = \exp(-x)\sin(y)
Yes
u(x,y) = e^y\cos(x); v(x,y) = e^y\sin(x)
Yes
u(x,y) = x^3 - 3xy^2; v(x,y) = 3x^2y - y^3
Yes
u(x,y) = \cos(x)\cosh(y); v(x,y) = -\sin(x)\sinh(y)
Yes
u(x,y) = \sin(x)\sinh(y); v(x,y) = \cos(x)\cosh(y)
No
u(x,y) = e^x\cos(y); v(x,y) = e^x\sin(y)
Yes
u(x,y) = \cos(x)\sinh(y); v(x,y) = \sin(x)\cosh(y)
No
u(x,y) = y^2 - x^2; v(x,y) = 2xy
Yes
u(x,y) = y^3 - 3x^2y; v(x,y) = 3xy^2 - x^3
Yes
u(x,y) = \cosh(x)\sin(y); v(x,y) = \sinh(x)\cos(y)
Yes
u(x,y) = \ln(x^2 + y^2); v(x,y) = \arctan\left(\frac{y}{x}\right)
No
u(x,y) = \ln\left(\sqrt{x^2 + y^2}\right); v(x,y) = \arctan\left(\frac{y}{x}\right)
Yes
u(x,y) = \sinh(x)\cos(y); v(x,y) = \cosh(x)\sin(y)
Yes
u(x,y) = \frac{3x^2y}{x^2+y^2}; v(x,y) = x^3 - 3xy^2
No
u(x,y) = \cos(x^2-y^2); v(x,y) = \sinh(2xy)
No
u(x,y) = \frac{x}{x^2 - y^2}; v(x,y) = \frac{y}{2xy}
No
u(x,y) = \sin(x^2 + y^2); v(x,y) = \cos(x^2 + y^2)
No
u(x,y) = y\cos(x); v(x,y) = x\sin(y)
No
u(x,y) = \sin(x)\exp(y); v(x,y) = -\cos(x)\exp(y)
Yes
© Hypatia.Tech. 2024 All rights reserved.