cauchy riemann equations
TRANSCRIPT
Cauchy-Riemann Equation
ππ
π π§=ππ
ππ₯
ππ₯
π π§+ππ
ππ¦
ππ¦
π π§
Cauchy-Riemann Equation
ππ
π π§=ππ
ππ₯
ππ₯
π π§+ππ
ππ¦
ππ¦
π π§
Cauchy-Riemann Equation
ππ
π π§=ππ
ππ₯
ππ₯
π π§+ππ
ππ¦
ππ¦
π π§
Cauchy-Riemann Equation
ππ
π π§=ππ
ππ₯
1
2+ππ
ππ¦
π
2
β΄ π₯ =π§ + π§
2, π¦ =
π§ β π§
2π
Cauchy-Riemann Equation
ππ
π π§=ππ
ππ₯
1
2+ππ
ππ¦
π
2
β΄ π₯ =π§ + π§
2, π¦ =
π§ β π§
2π
Cauchy-Riemann Equation
ππ
π π§=1
2
ππ
ππ₯+ π
ππ
ππ¦
β΄ π₯ =π§ + π§
2, π¦ =
π§ β π§
2π
Cauchy-Riemann Equation
π π§ is holomorphic βΊππ
ππ₯=
ππ
ππy
β
ππ
π π§=1
2
ππ
ππ₯+ π
ππ
ππ¦=1
2
ππ
πππ¦+ π
ππ
ππ¦= 0
Cauchy-Riemann Equation
π π§ is holomorphic βΊππ
ππ₯=
ππ
ππy
β
ππ
π π§=1
2
ππ
ππ₯+ π
ππ
ππ¦=1
2
ππ
πππ¦+ π
ππ
ππ¦= 0
Cauchy-Riemann Equation
π π§ is holomorphic βΊππ
ππ₯=
ππ
ππy
β
ππ
π π§=1
2
ππ
ππ₯+ π
ππ
ππ¦=1
2
ππ
πππ¦+ π
ππ
ππ¦= 0
Cauchy-Riemann Equation
π π§ is holomorphic βΊππ
ππ₯=
ππ
ππy
β
ππ
π π§=1
2
ππ
ππ₯+ π
ππ
ππ¦=1
2
ππ
πππ¦+ π
ππ
ππ¦= 0
Cauchy-Riemann Equation
π π§ is holomorphic βΊππ
ππ₯=
ππ
ππy
β
ππ
π π§=1
2
ππ
ππ₯+ π
ππ
ππ¦=1
2βπ
ππ
ππ¦+ π
ππ
ππ¦= 0
Cauchy-Riemann Equation
β΄ π π§ is holomorphic βππ
π π§= 0
ππππ¦ π πππππ!
Cauchy-Riemann Equation
β΄ π π§ is holomorphic βππ
π π§= 0
ππππ¦ π πππππ!
Exercise
Is π§ 3 holomorphic function?
Answer
π π§ = π§ 3 = π§ π§32 β
ππ
π π§=3
2π§32 π§ β 0
β΄ π§ 3 is not holomorphic function.
Exercise
Is π§ 3 holomorphic function?
Answer
π π§ = π§ 3 = π§ π§32 β
ππ
π π§=3
2π§32 π§ β 0
β΄ π§ 3 is not holomorphic function.
Exercise
Is π§ 3 holomorphic function?
Answer
π π§ = π§ 3 = π§ π§32 β
ππ
π π§=3
2π§32 π§ β 0
β΄ π§ 3 is not holomorphic function.
Exercise
Is π§ 3 holomorphic function?
Answer
π π§ = π§ 3 = π§ π§32 β
ππ
π π§=3
2π§32 π§ β 0
β΄ π§ 3 is not holomorphic function.