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complex_line_integral [2015/02/03 09:55] nikolaj |
complex_line_integral [2015/04/03 12:15] nikolaj |
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==== Function ==== | ==== Function ==== | ||
| @#DDDDDD: range | @#DDDDDD: $\mathcal{L}$ ... continuously differentiable finite lines | | | @#DDDDDD: range | @#DDDDDD: $\mathcal{L}$ ... continuously differentiable finite lines | | ||
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| @#FFBB00: definiendum | @#FFBB00: $\int: \mathcal{L}\to(\mathbb C\to \mathbb C)\to \mathbb K$ | | | @#FFBB00: definiendum | @#FFBB00: $\int: \mathcal{L}\to(\mathbb C\to \mathbb C)\to \mathbb K$ | | ||
+ | | @#DDDDDD: range | @#DDDDDD: $L\in \mathcal{L}$ | | ||
+ | | @#DDDDDD: range | @#DDDDDD: $\gamma: [a,b]\to L$ ... parametrization | | ||
+ | | @#FFBB00: definiendum | @#FFBB00: $\int_L\ f(z)\,\mathrm dz:=\int_L\ f\left(\gamma(t)\right)\cdot \gamma'(t)\, \mathrm dt$ | | ||
- | | @#DDDDDD: range | @#DDDDDD: $L\in \mathcal{L}$ | @#DDDDDD: range | @#DDDDDD: $\gamma: [a,b]\to L$ ... parametrization | | + | >todo: [[Continuously differentiable finite lines]] |
- | + | ||
- | | @#FFBB00: definiendum | @#FFBB00: $\int_L\ f(z)\,\mathrm dz:=\int_L\ f\left(\gamma(t)\right)\cdot \gamma'(t)\, \mathrm dt$ | | + | |
----- | ----- | ||
- | >todo: [[Continuously differentiable finite lines]] | ||
=== Theorems === | === Theorems === | ||
If $f$ is holomorphic and two curves $L_1,L_2$ can be deformed into each other, then | If $f$ is holomorphic and two curves $L_1,L_2$ can be deformed into each other, then |