Cauchy–Riemannn.

/ˌkəʊʃɪˈriːmən/

Etymology: < the names of Augustin-Louis Cauchy (see Cauchy n.) and G. F. Bernhard Riemann (see Riemann n.).

Mathematics.

Cauchy–Riemann equations n. 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

ΘΚΠ

the world > relative properties > number > calculus > [noun] > differential calculus > differential equations

Cauchy–Riemann equations1914

Mathieu's equation1915

1914 S. E. Rasor tr. Burkhardt 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: {^∂u/ _∂r = ⁱ/ _r·^∂v/ _∂ϕ, ^∂v/ _∂r = − ⁱ/ _r·^∂u/ _∂ϕ.

1929 Encycl. 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.

1968 C. G. Kuper Introd. Theory Superconductivity v. 82 Equations..have the form of Cauchy–Riemann equations for the function h=dw/dz.

This entry has not yet been fully updated (first published 1997; most recently modified version published online June 2018).

单词	cauchy–riemann
释义	Cauchy–Riemannn. /ˌkəʊʃɪˈriːmən/ Etymology: < the names of Augustin-Louis Cauchy (see Cauchy n.) and G. F. Bernhard Riemann (see Riemann n.). Mathematics. Cauchy–Riemann equations n. 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 ΘΚΠ the world > relative properties > number > calculus > [noun] > differential calculus > differential equations Cauchy–Riemann equations1914 Mathieu's equation1915 1914 S. E. Rasor tr. Burkhardt 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: {^∂u/ _∂r = ⁱ/ _r·^∂v/ _∂ϕ, ^∂v/ _∂r = − ⁱ/ _r·^∂u/ _∂ϕ. 1929 Encycl. 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. 1968 C. G. Kuper Introd. Theory Superconductivity v. 82 Equations..have the form of Cauchy–Riemann equations for the function h=dw/dz. This entry has not yet been fully updated (first published 1997; most recently modified version published online June 2018). < n.1914
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