Starting with Interlude 2, and continuing through Interludes 3 and 4, we will investigate how our ability to understand and calculate derivatives lends itself to some powerful modeling applications in the real world.

These notes for Interlude 2 introduce “differential equations” (DE’s) and “initial value problems” (IVP’s), and the important idea that even though solving differential equations is hard, with our knowledge of derivatives we can already investigate a lot of important cases. We then begin to explore some real world application of exponential growth models, and how they can be understood as a differential equation.

For a more thorough explanation of what it means for a function to be a solution to a DE or IVP, please watch Video TT2a: Differential Equations on the Math Department YouTube page.

As the semester progresses, we will collect below some supplemental notes and exercises, which will introduce some important applications of differential equations to various other disciplines, all of which are accessible to a student with knowledge of Chapters 1 and 2 of the text.