Unit · year 2
MU-206 · Complex Analysis
Threads change · space6 theorems
How complex differentiability forces astonishing rigidity and power.
Theorems in this unit
T-068
The Cauchy–Riemann equations
Complex differentiability is equivalent to a pair of PDEs.
T-069
Cauchy's integral theorem
The integral of a holomorphic function round a closed loop is zero.
T-070
Cauchy's integral formula
A holomorphic function's values are determined by its boundary values.
T-071
Liouville's theorem
A bounded entire function is constant.
T-072
The fundamental theorem of algebra
Every non-constant polynomial over C has a root.
T-073
The residue theorem
A contour integral equals the sum of enclosed residues.