· 5 min
Residues and Contour Integration
Evaluating integrals by what a function leaves behind at its poles. The Laurent series and the residue, the residue theorem, and a contour computation of the Cauchy characteristic function.
#complex-analysis
· 8 min
Holomorphic Functions and Cauchy's Theorem
Why complex differentiability is so much stronger than real. The Cauchy-Riemann equations, Goursat's vanishing contour integral, the Cauchy integral formula recovering a function from its boundary values, and the analyticity and Liouville theorems that follow.