Geometric harmonic analysis ; 3: Integral representations Calderón Zygmund theory Fatou theorems and applications to scattering This monograph presents a comprehensive self contained and novel approach to the Divergence Theorem through five progressive volumes. Its ultimate aim is to develop tools in Real and Harmonic Analysis of geometric measure theoretic flavor capable of treating a broad spectrum of boundary value problems formulated in rather general geometric and analytic settings. The text is intended for researchers graduate students and industry professionals interested in applications of harmonic analysis and geometric measure theory to complex analysis scattering and partial differential equations. Volume III is concerned with integral representation formulas for nullsolutions of elliptic PDEs Calderón Zygmund theory for singular integral operators Fatou type theorems for systems of elliptic PDEs and applications to acoustic and electromagnetic scattering. Overall this amounts to a powerful and nuanced theory developed on uniformly rectifiable sets which builds on the work of many predecessors.