Nov 3, 2025
A fun application of Green's functions and geometric algebra: Residue calculus
[Click here for a PDF version of this post] Motivation. A fun application of both Green’s functions and geometric algebra is to show how the Cauchy integral equation can be expressed in terms of the Green’s function for the 2D gradient. This is covered, almost as an aside, in [1]. I found that treatment a bit hard to understand, so I am going to work through it here at my own pace. Complex…
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#area integral#Cauchy equation#Cauchy integral equation#Cauchy kernel#complex numbers#delta function#even grade multivector#Fundamental Theorem of Geometric Calculus#Geometric Algebra#Geometric Calculus#gradient#Green&039;s function#imaginary#Laplacian#line integral#multivector#oriented area#pseudoscalar#residue