Spatial Models

Mathematical Modeling · Axiom Academy

Discover how mathematical models capture phenomena that vary across space, not just time Beyond Time: Adding Space to Our Models So far, our models have tracked how quantities change over time. But what about phenomena that vary across space? Click "Run Both Models" to see the difference. One of the most fundamental spatial processes is diffusion - the tendency of substances to spread out from regions of high concentration to low concentration. Click anywhere on the canvas to add a drop and watch it spread! Click anywhere to add drops of "dye" Spatial models help us understand the remarkable patterns we observe in nature and human systems. Click each example to discover how spatial mathematics explains these phenomena. Spatial models use partial differential equations (PDEs) - equations involving derivatives with respect to both space and time. Click each card to reveal the fundamental equations you'll learn in this unit.

This is the written version of the interactive lesson above. See the full Mathematical Modeling course.