Euler’s method - How to use it?
Euler’s method is a numerical method that you can use to approximate the solution to an initial value problem with a differential equation that can’t be solved using a more traditional method, like the methods we use to solve separable, exact, or linear differential equations.
From the way we study differential equations, we tend to think that all differential equations fit into one of these neat categories. In fact, these special cases are the exception, not the rule. The vast majority of differential equations don’t fit these formats, and we don’t have a convenient way to solve them with calculus. When that’s the case, we can use a numerical method instead to approximate the value of the solution. Euler’s method is one of the most common numerical methods, and gives us a way to approximate the solution to a differential equation initial value problem.
In this video you'll learn:
0:00 // What is Euler’s method?
0:22 // When to use Euler’s method?
2:24 // How to use Euler’s method?
5:40 // How to find each piece of Euler’s method formula?
18:04 // Why does Euler’s method work?
26:47 // When does Euler’s method fail? (When you can’t use Euler’s method)
30:47 // When is Euler’s method an underestimate? When is it an overestimate?
33:14 // How accurate is Euler’s method?
33:45 // What is the error formula for Euler’s method?
