Profile and plan curvature are standard tools in geomorphometry. Streamline curvature has not been as widely used but is a natural counterpart to plan curvature. Expressions for all three types of curvature can be easily derived using the concept of a directional derivative. Various types of curvature can sometimes be used to make general statements about the solutions to a PDE (partial differential equation). Examples are given to show how nonlinear, first and second-order PDEs can be manipulated with simple algebra to get expressions regarding their solutions in terms of curvatures. These expressions are powerful in that they allow us to use our intuitive, geometric understanding of curvature concepts to better understand nonlinear PDEs for which it is often difficult to obtain analytical or numerical solutions.