| 释义 |
Cauchy–Riemann, n. Math.|ˌkəʊʃɪˈriːmən|
[The names of Augustin-Louis Cauchy (see *Cauchy n.) and G. F. Bernhard Riemann (see Riemann n.).]
Cauchy–Riemann equations, the partial differential equations which must be satisfied if a function f(x, y) of two variables, separable into a real part u and an imaginary part v, is to be analytic, namely the two equations ∂u / ∂x = ∂v / ∂y and ∂u / ∂y = - ∂v / ∂x .
1914S. E. Rasor tr. Burkhardt's Theory of Functions of Complex Variable iv. 181 Prove by passing directly to the limit that in polar coördinates the Cauchy–Riemann differential equations take the form: {ob} ∂u / ∂r = i / r · ∂v / ∂ϕ , ∂v / ∂r = - i / r · ∂u / ∂ϕ . 1929Encycl. Brit. IX. 919/2 The Cauchy–Riemann equations and Laplace's equation are of central importance in the theory of maps and in various problems of mathematical physics. 1968C. G. Kuper Introd. Theory Superconductivity v. 82 Equations..have the form of Cauchy–Riemann equations for the function h= dw/dz . |