The Real World: Differential Equations

The Real World: Differential Equations

Mathematics can be used, and is used, to describe the physical phenomena of the world we live in. Differential equations are an application of the ideas of calculus to our everyday lives. In differential equations we seek to model real-life situations in Mathematical terms. Thus, differential equations are used for scientific modeling to describe the dynamics of diverse state variables, such as daily temperature, proportion of a population infected by influenza, chemical concentration in a tank, or stock prices by observing real-time data. Once the model is created it is used as a representation of the real-world system and predictions about future states and both observable and unobservable behaviors can be made. The tools of modeling and utilization of analytic, qualitative, and numerical techniques for solving differential equations allow for an unlocking of the world’s mysteries. We utilize the techniques of differential equations to study problems in immunology and the famous 1940 collapse of the Tacoma Narrows bridge.