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4]Cauchy Riemann (CR) Equations - Complex Analysis - Engineering Mathematics
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Cauchy Riemann Equations
In last video we studied, what are analytic functions? To check whether the function is analytic or not, that is given by Cauchy Riemann (CR) Equations.
What is Cauchy Riemann Equations
Statement is suppose f(z)= u(x,y) + i(x,y) is differentiable at point z = x + iy then at z, first order partial derivative of u and v exist and satisfy Cauchy - Riemann Equations.
To check whether the function is analytic or not, it should satisfy Cauchy - Riemann (CR) Equation. This is not the only condition to be checked, there is one more condition.
Conditions:
Four partial derivatives ux, uy, vx, vy exist and all are continuous.
ux = vy and uy = -vx
Two examples based on CR equation or whether function is analytic or not is explained in the video tutorial.
In last video we studied, what are analytic functions? To check whether the function is analytic or not, that is given by Cauchy Riemann (CR) Equations.
What is Cauchy Riemann Equations
Statement is suppose f(z)= u(x,y) + i(x,y) is differentiable at point z = x + iy then at z, first order partial derivative of u and v exist and satisfy Cauchy - Riemann Equations.
To check whether the function is analytic or not, it should satisfy Cauchy - Riemann (CR) Equation. This is not the only condition to be checked, there is one more condition.
Conditions:
Four partial derivatives ux, uy, vx, vy exist and all are continuous.
ux = vy and uy = -vx
Two examples based on CR equation or whether function is analytic or not is explained in the video tutorial.
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