In this interlude, we will investigate a famous and simple way to model temperature using differential equations, known as “Newton’s Law of Cooling”. Although the situation is much more complicated in reality (see Heat Equation), we can already understand the calculus behind Newton’s Law of Cooling, which is a very useful approximation in many situations….
Tag: interlude
Interlude 3 – Slope Fields
For any differential equation of the form dy/dx = f(x,y), we can construct a “slope field” for the differential equation, which allows us to understand the qualitative behavior of the solutions without needing to know a formula for the solutions. The following set of notes introduces the main ideas, and has some exercises for you…
Interlude 2 – Introduction to Differential Equations
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…
Newton’s Method
The handout below contains a summary of the important points about Newton’s Method, as well as introduces the Bisection Method for comparison. There are some exercises at the end for you to test your understanding of some of the important ideas. This Desmos graph gives a visual representation of what is going on during each…