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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Complex contour integrals
Complex integration accumulates function values along an oriented parameterized curve.
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Cauchy integral formula
Contour values determine interior values and derivatives of a holomorphic function under the contour hypotheses.
Complex numbers
A complex number has real and imaginary parts and is represented on the complex plane.
Residue theorem
A contour integral equals two pi i times enclosed residues under the theorem's hypotheses.
Residues
The coefficient of power minus one in a Laurent expansion controls a local contour integral.
Analytic continuation
Compatible holomorphic functions extend an analytic function to larger connected regions.
Knowledge connections
- Cauchy integral formula · Related · Map context
- Residues · Related · Map context
- Complex numbers · Related · Map context
- Residue theorem · Related · Map context