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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Residues
The coefficient of power minus one in a Laurent expansion controls a local contour integral.
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Complex contour integrals
Complex integration accumulates function values along an oriented parameterized curve.
Isolated singularities
A punctured neighborhood can contain a removable singularity, a pole or an essential singularity.
Laurent series
A Laurent series uses positive and negative powers on an annulus.
Residue theorem
A contour integral equals two pi i times enclosed residues under the theorem's hypotheses.
Analytic continuation
Compatible holomorphic functions extend an analytic function to larger connected regions.
Knowledge connections
- Isolated singularities · Related · Map context
- Complex contour integrals · Related · Map context
- Laurent series · Prerequisite · Map context
- Residue theorem · Next concept · Map context