Complex Analysis
Explore complex functions; integration and singularities; mappings and global behavior. Concepts and connections are available independently of video coverage.
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Residue theorem
A contour integral equals two pi i times enclosed residues under the theorem's hypotheses.
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Analytic continuation
Compatible holomorphic functions extend an analytic function to larger connected regions.
Complex contour integrals
Complex integration accumulates function values along an oriented parameterized curve.
Conformal maps
A holomorphic map with nonzero derivative locally preserves oriented angles.
Derivatives
A derivative is the limit of a difference quotient, measuring local rate of change when that limit exists.
Residues
The coefficient of power minus one in a Laurent expansion controls a local contour integral.
Knowledge connections
- Conformal maps · Related · Map context
- Analytic continuation · Related · Map context
- Complex contour integrals · Related · Map context
- Derivatives · Related · Map context
- Residues · Prerequisite · Map context