Differential Equations: Population Growth (DTube)

In this video I go over an introduction to differential equations and explain a bit about how they are the most important applications of calculus to the real-world. Differential equations are simply equations that consist of a function and some of its derivatives. These types of equations model real-world applications very well because often times physical concepts change at a rate that is proportional to its current state.

One such example is in population growth in which the rate of growth depends on what the current population is. In this video I use differential equations to model population growth. The first differential equation for population growth that I go over is for ideal conditions and is simply stated as the rate of growth is proportional to the current population. But a more accurate model assumes that there is a maximum carrying capacity in which the population levels off. This latter model is known as the Logistic Differential Equation and was first proposed by the Dutch mathematical biologist Pierre-François Verhulst in the 1840s. I also go over a brief history lesson on Verhulst.

This is an extremely important video as it lays the foundation for my later videos on one of the most powerful mathematical concepts, differential equations, so make sure to watch this video!

Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhsEMZvMcUkjvxzId8g

View Video Notes on Steemit: https://steemit.com/mathematics/@mes/differential-equations-population-growth