Cauchy-Riemann Equations
Source lecture(s): PHY622 Lec3
Physical Meaning
Necessary and sufficient conditions for complex differentiability.
Variable Definitions
| Symbol | Meaning |
|---|---|
| \(u\) | real part |
| \(v\) | imaginary part |
Assumptions
\(u,v\) have continuous partial derivatives.
Derivation
Equate limits along real and imaginary axes in \((f(z+\Delta z)-f(z))/\Delta z\).
Applications
Testing analyticity, fluid dynamics (potential flow), electrostatics.
Connections to Other Equations
- analytic-functions
- conformal-mapping