10/30/2008: Intro. to differential equations, solutions to differential equations, Euler’s method

1. Main Points
In today’s reading I learned about differential equations which are employed when one does not know a key function but has information about its rate of change or its derivative. This information is then used to write a differential equation from which one can get information about the original function. A solution to a differential equation is any function that satisfies the differential equation.

2. Challenging
I did not quite understand how we check a solution to a differential by substituting the solution into the left and right sides of the equation separately.

3. Intriguing
I found the example of a population in confined space growing proportionally to the product of the current population, P, and the difference between the carrying capacity, L, and the current population, to be really cool. This can definitely be applied to bacteria growing in a petrie dish for example!