complex-analysis
Contour integration
taught
Integrating a complex function along a parametrized path in the plane, built from an ordinary Riemann sum in the limit.
Taught in
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Contours and parametrization
Complex Analysis
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Contour integrals
Complex Analysis
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Properties of contour integrals and the ML inequality
Complex Analysis
Requires
- complex-continuity required
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complex-differentiability
helpful
Most contours worth integrating over run through a region where the integrand is analytic, though continuity alone is what the definition needs.
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line-integrals-of-vector-fields-and-work
helpful
The real-variable line integral this construction generalizes -- a complex contour integral splits into the same real/imaginary parametrized-path sums.
Required by
- Cauchy-Goursat theorem required
- Evaluating real integrals with residues required
- Path independence and complex antiderivatives required
- The ML inequality required
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Local knowledge map
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