This document provides a derivation of all equations mentioned in the main text of the article "Arterial pulse wave modelling and analysis for vascular age studies: a review from VascAgeNet". Starting from the full three-dimensional (3-D) Navier Stokes equations, we provide a detailed derivation of (i) the nonlinear one-dimensional (1-D) governing equations of arterial blood flow (Section 2.1), (ii) their theoretical analysis using the method of characteristics from which several pulse wave analysis methods can...