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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Holomorphic functions
A function is holomorphic when complex differentiable throughout an open neighborhood.
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Cauchy–Riemann equations
Complex differentiability imposes relations between real and imaginary partial derivatives.
Complex exponentials
Euler's formula links complex exponentials to cosine and sine for real angles.
Complex numbers
A complex number has real and imaginary parts and is represented on the complex plane.
Derivatives
A derivative is the limit of a difference quotient, measuring local rate of change when that limit exists.
Analytic continuation
Compatible holomorphic functions extend an analytic function to larger connected regions.
Knowledge connections
- Complex exponentials · Related · Map context
- Cauchy–Riemann equations · Related · Map context
- Complex numbers · Prerequisite · Map context
- Derivatives · Prerequisite · Map context