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complex_line_integral [2015/02/03 09:58] nikolaj |
complex_line_integral [2015/04/03 12:15] nikolaj |
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| | @#DDDDDD: range | @#DDDDDD: $\mathcal{L}$ ... continuously differentiable finite lines | | | @#DDDDDD: range | @#DDDDDD: $\mathcal{L}$ ... continuously differentiable finite lines | | ||
| | @#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 | | + | | @#DDDDDD: range | @#DDDDDD: $L\in \mathcal{L}$ | |
| + | | @#DDDDDD: range | @#DDDDDD: $\gamma: [a,b]\to L$ ... parametrization | | ||
| | @#FFBB00: definiendum | @#FFBB00: $\int_L\ f(z)\,\mathrm dz:=\int_L\ f\left(\gamma(t)\right)\cdot \gamma'(t)\, \mathrm dt$ | | | @#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]] | >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 | ||
