Complex Variables · Calculus

Cauchy’s Theorem and Integral Formula

Cauchy’s theorem: the integral of an analytic function around a closed curve is zero. From this flows Liouville’s theorem (bounded entire ⇒ constant) and the FTA.

WHAT STUDENTS WILL LEARN

✓Prove Cauchy’s integral theorem for simply connected domains

✓Apply Cauchy’s integral formula

✓Derive infinite differentiability of analytic functions

✓Prove Liouville’s theorem and FTA

BUILDS ON

Complex Numbers and Analytic FunctionsComplex Variables Line Integrals and Green’s TheoremCalculus III

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