![]() ![]() Using Euler’s Method is like detective work. On the other hand, why stop at just one step? Once you know the value of y 1, then you can use that value in a similar way to find out y 2. If you’re only going from t 0 to t 1 (a single step), then you get: That means that you can replace y ‘ by its current value as determined by the function f. The final piece of the puzzle is to use the given information that y ‘ = f( t, y). Letting the difference in time be h = t 1 – t 0, then the formula becomes: ![]() Now if y changes from y 0 to y 1 in the time interval from t 0 to t 1, then we can express this fact using the derivative: So even if you don’t know what y is, if you can tell how fast it’s changing, then that info can help you to build up the values of y. The key is that the y ‘ always measures the rate of change of the function y. In fact, a good grasp of the theory helps you in other areas of calculus as well. It’s helpful to understand a little of the theory behind Euler’s Method. Then the solution at later times t 1, t 2, t 3, … can be found using the following algorithm. The given time t 0 is the initial time, and the corresponding y 0 is the initial value.įirst, you must choose a small step size h (which is almost always given in the problem statement on the AP exam). ![]() Euler’s MethodĮuler’s Method is a step-based method for approximating the solution to an initial value problem of the following type. What is Euler’s Method? In this post we review this technique for approximating solutions to certain kinds of differential equations and work out a few examples based on what you may see on the AP Calculus BC exam. ![]()
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