The Newton-Raphson solution of a nonlinear system iterately linearizes the equations, then steps to the solution of the resulting affine model. When a step exceeds the predictive range of its model, the method can diverge.  The traditional response -- aggregating the equations into a cost function, and applying a minimization method -- suppresses information about how each equation model performs. Direct error measures examine the equations individually, allowing finer control over step lengths.  The seminar will develop one such measure through the geometry of simple one- and two-dimensional examples, then present results from a suite of larger systems. Airflow problems typical of building energy solvers exhibit special properties that reduce the computational cost of applying such methods.