微分:定义 若函数=f(z)在z点的改变量 △=f(z+4z)-f(z)可以写成 △=A(2)4z+p(42) 其中 p(△z) 0 →0△z 则称=f()在z点可微,△的线性部分 A(2)△2称为函数在点的微分,记作 d=A()dz约定dz=4z
Analytic Functions Elementary Functions Differentiability Analyticity ©µ½Â e¼êw = f(z)3z:UCþ ∆w = f(z + ∆z) − f(z)±¤ ∆w = A(z)∆z + ρ(∆z) Ù¥ lim ∆z→0 ρ(∆z) ∆z = 0 K¡w = f(z)3z: §∆w5Ü© A(z)∆z¡¼êw3z:©§P dw = A(z)dz ½dz = ∆z C. S. Wu 1ù )Û¼ê
微商 可以证明,若函数=∫(x)在z点可导,则一定 在该点可微,反之亦然开且A(2)=(2),即
Analytic Functions Elementary Functions Differentiability Analyticity û ±y²§e¼êw = f(z)3z:§K½ 3T: §½, ¶¿ A(z) = f 0 (z)§= dw = f 0 (z) dz ½ dw dz = f 0 (z) Ïdê¡û C. S. Wu 1ù )Û¼ê
微商 可以证明,若函数=f()在z点可导,则一定 在该点可微,反之亦然;并且A(2)=f(2),即 du=f(2)d2或
Analytic Functions Elementary Functions Differentiability Analyticity û ±y²§e¼êw = f(z)3z:§K½ 3T: §½, ¶¿ A(z) = f 0 (z)§= dw = f 0 (z) dz ½ dw dz = f 0 (z) Ïdê¡û C. S. Wu 1ù )Û¼ê
微商 可以证明,若函数=f()在z点可导,则一定 在该点可微,反之亦然;并且A(z)=f(z),即 du d=f()dz或
Analytic Functions Elementary Functions Differentiability Analyticity û ±y²§e¼êw = f(z)3z:§K½ 3T: §½, ¶¿ A(z) = f 0 (z)§= dw = f 0 (z) dz ½ dw dz = f 0 (z) Ïdê¡û C. S. Wu 1ù )Û¼ê
微商 可以证明,若函数=f()在z点可导,则一定 在该点可微,反之亦然;并且A(z)=f(z),即 du d=f()dz或 因此导数也称作微商
Analytic Functions Elementary Functions Differentiability Analyticity û ±y²§e¼êw = f(z)3z:§K½ 3T: §½, ¶¿ A(z) = f 0 (z)§= dw = f 0 (z) dz ½ dw dz = f 0 (z) Ïdê¡û C. S. Wu 1ù )Û¼ê