Linear Approximations
N2O5 is a reagent that was used synthesize explosives like TNT. Unfortunately, N2O5 decomposes relatively quickly at or above room temperature, so if you accidentally leave a bottle of it out on the counter, you could be in trouble! In this video, we'll approximate a solution to the decomposition rate equation to figure out whether a batch of N2O5 that you left at room temperature can still be used. We'll also determine under what conditions our approximation is valid. This video is part of the Linearity video series. Many complex systems are modeled or approximated linearly because of the mathematical advantages. Hi, my name is Ben Brubaker, and I'm a professor in the Department of Mathematics at MIT. Today we'll be talking about linear approximations. In mathematical terms, this is just another name for the tangent line to a function. But the name suggests more. Linear approximations can be used to simplify mathematical models that are not analytically s...