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complex_line_integral [2014/03/21 11:11] 127.0.0.1 external edit |
complex_line_integral [2015/02/03 09:58] 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: $\int: \mathcal{L}\to(\mathbb C\to \mathbb C)\to \mathbb K$ | | ||
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| @#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 | | ||
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| @#FFBB00: definiendum | @#FFBB00: $\int_L\ f(z)\,\mathrm dz:=\int_L\ f\left(\gamma(t)\right)\cdot \gamma'(t)\, \mathrm dt$ | | | @#FFBB00: definiendum | @#FFBB00: $\int_L\ f(z)\,\mathrm dz:=\int_L\ f\left(\gamma(t)\right)\cdot \gamma'(t)\, \mathrm dt$ | | ||
- | ==== Discussion ==== | + | ----- |
>todo: [[Continuously differentiable finite lines]] | >todo: [[Continuously differentiable finite lines]] | ||
=== Theorems === | === Theorems === | ||
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== Fundamental theorem of calculus == | == Fundamental theorem of calculus == | ||
^ $\int_L f'(z)\,\mathrm dz=f(b)-f(a)$ ^ | ^ $\int_L f'(z)\,\mathrm dz=f(b)-f(a)$ ^ | ||
- | ==== Parents ==== | + | |
+ | ----- | ||
=== Requirements === | === Requirements === | ||
[[Function integral]], [[Integral over a subset]] | [[Function integral]], [[Integral over a subset]] |