Bogart Other Mul 根式函数√z的多值性 给定一个自变量值z,凡是满足等式2=z的u 值,就是根式函数√z的函数值,或者说,是z的 平方根
Root Functions Logarithmic Functions Other Multivalued Functions Multivalued Property of Root Functions Branching Points in Root Functions Branch Cut of Root Functions Riemann Surface of Root Functions ª¼ê √ zõ5 ½Â ½gCþz§ ´÷v ªw 2 = zw §Ò´ª¼ê √ z¼ê§½ö`§´z ² §´¼êz 2 = w=w = z 2¼ê §õ5Ly3µéAugCþz§ ª¼ê √ zü Ù/wѪ¼ê5§Ic [©Ûe¼êw = √ z − a C. S. Wu 1nù õ¼ê
Bogart Other Mul 根式函数√z的多值性 给定一个自变量值z,凡是满足等式2=z的u 值,就是根式函数√z的函数值,或者说,是z的 平方根 它是幂函数z2=即=2的反函数 它的多值性表现在:对应于一个自变量值 根式函数√可取两个值
Root Functions Logarithmic Functions Other Multivalued Functions Multivalued Property of Root Functions Branching Points in Root Functions Branch Cut of Root Functions Riemann Surface of Root Functions ª¼ê √ zõ5 ½Â ½gCþz§ ´÷v ªw 2 = zw §Ò´ª¼ê √ z¼ê§½ö`§´z ² §´¼êz 2 = w=w = z 2¼ê §õ5Ly3µéAugCþz§ ª¼ê √ zü Ù/wѪ¼ê5§Ic [©Ûe¼êw = √ z − a C. S. Wu 1nù õ¼ê
Bogart Other Mul 根式函数√z的多值性 给定一个自变量值z,凡是满足等式2=z的u 值,就是根式函数√z的函数值,或者说,是z的 平方根 它是幂函数2=即=2的反函数 它的多值性表现在:对应于一个自变量值z, 根式函数√z可取两个值 为了更清是地看出根式函数的性质,需要仔(类 细分析一下函数=√2-0
Root Functions Logarithmic Functions Other Multivalued Functions Multivalued Property of Root Functions Branching Points in Root Functions Branch Cut of Root Functions Riemann Surface of Root Functions ª¼ê √ zõ5 ½Â ½gCþz§ ´÷v ªw 2 = zw §Ò´ª¼ê √ z¼ê§½ö`§´z ² §´¼êz 2 = w=w = z 2¼ê §õ5Ly3µéAugCþz§ ª¼ê √ zü Ù/wѪ¼ê5§Ic [©Ûe¼êw = √ z − a C. S. Wu 1nù õ¼ê
Bogart Other Mul 根式函数√z的多值性 给定一个自变量值z,凡是满足等式2=z的u 值,就是根式函数√z的函数值,或者说,是z的 平方根 它是幂函数2=即=2的反函数 ρ它的多值性表现在:对应于一个自变量值z, 根式函数√之可取两个值 为了更清楚地看出根式函数的性质,需要仔( 细分析一下函数=√z-a
Root Functions Logarithmic Functions Other Multivalued Functions Multivalued Property of Root Functions Branching Points in Root Functions Branch Cut of Root Functions Riemann Surface of Root Functions ª¼ê √ zõ5 ½Â ½gCþz§ ´÷v ªw 2 = zw §Ò´ª¼ê √ z¼ê§½ö`§´z ² §´¼êz 2 = w=w = z 2¼ê §õ5Ly3µéAugCþz§ ª¼ê √ zü Ù/wѪ¼ê5§Ic [©Ûe¼êw = √ z − a C. S. Wu 1nù õ¼ê
Bogart Other Mul 根式函数= a的多值性 采用极坐标表达式=pe°,z-a=re 代入则有
Root Functions Logarithmic Functions Other Multivalued Functions Multivalued Property of Root Functions Branching Points in Root Functions Branch Cut of Root Functions Riemann Surface of Root Functions ª¼êw = √ z − aõ5 æ^4ILªw = ρe iφ , z − a = re iθ \Kk ρ = √ r φ = θ 2 + nπ n = 0, ±1, ±2, · · · Ïd§éu½z§küw éAµ w1(z) =√ re iθ/2 un = 0, ±2, · · · w2(z) =√ re i(π+θ/2) = − √ re iθ/2 un = ±1, ±3, · · · C. S. Wu 1nù õ¼ê