MJMAUDℓℓ ℓLSBℓAFℓ SℓIALMDSTX A M N D T. D. Ef(x, y ) =e x 2 −y 2 sin(2xy). ff′ x (x, y ) = (2x sin(2xy) + 2 ycos(2xy)) e x 2 −y 2 , f′′ x 2 (x, y ) = (4x 2 −4y 2 + 2) si n(2 xy) + 8xycos(2xy) e x 2 −y 2 . f′ y (x, y ) = (−2ysin(2xy) + 2x cos(2 xy)) e x 2 −y 2 , f′′ y 2 (x, y ) = (−4x 2 + 4y 2 − 2) sin(2 xy) −8xycos(2xy) e x 2 −y 2 . ∆f(x, y ) =f′′ x 2 (x, y ) +f′′ y 2 (x, y ) = 0 fR 2 . EC C (z=x +iy x y f(z) = (2x 2 − 3x − 3iy) +i(4xy+ 2 iy 2 ). f(z) = (2x 2 − 3x − 3iy) + i(4xy+ 2iy 2 ) = (2x 2 − 3x − 2y 2 ) + i(4xy − 3y ) =P(x, y ) + iQ(x, y ). fPQ P′ x (x, y ) =Q ′ y (x, y ), P′ y (x, y ) =−Q ′ x (x, y ). P′ x (x, y ) = (2x 2 − 3x− 2y 2 ) ′ x = 4x −3, Q ′ y (x, y ) = (4xy −3y ) ′ y = 4x− 3, P′ y (x, y ) = (2x 2 −3x −2y 2 ) ′ y =−4y, Q ′ x (x, y ) = (4xy−3y ) ′ y = 4y, fC. f(z) = 2z2 −3zM
