| Abstract: | Mapping spatial change is a fundamental theme in geography. The analytical and numerical application of differential calculus to continuous geographic data produces first-derivative distributions that can be mapped to show gradient magnitude and gradient direction, and second-derivative measures that can be mapped to show the form (convexity, concavity) of the geographic surface. When these differential measures are obtained for spatially distributed temporal data, a velocity/acceleration change map can be constructed. Cartographic applications of the methodology presented in this paper include slope and curvature landform mapping, derivative trend-surface mapping of urban housing value gradients and the velocity/acceleration mapping of mobile-home residency in the United States from 1950 to 1980. |
