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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Isolated singularities
A punctured neighborhood can contain a removable singularity, a pole or an essential singularity.
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Laurent series
A Laurent series uses positive and negative powers on an annulus.
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.
Cauchy integral formula
Contour values determine interior values and derivatives of a holomorphic function under the contour hypotheses.
Cauchy–Riemann equations
Complex differentiability imposes relations between real and imaginary partial derivatives.
Knowledge connections
- Laurent series · Related · Map context
- Residues · Related · Map context