Differential Equations: Euler's Method

In my earlier videos I went over using direction fields to graphically approximate solutions to differential equations, but in this video I show how we can use direction fields to numerically approximate solutions as well. This process is called the Euler's Method and is quite simply approximating the solution to an initial-value problem by using straight line segments in which the slopes are determined at each point through the differential equation. I also show in the video that as we increase the number of line segments by shortening the step size between each point, then we effectively can get closer and closer to the exact solution. With computers, this is obviously very practical since they can solve many calculations at once, and in fact many super computers are used in numerically solving differential equations using similar methods as the Euler Method. This video gives a very important illustration of a very important concept, which is numerical approximation to differential equations, so make sure to watch this video!

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Differential Equations Direction Fields: Example 2: Electric Circuit: https://youtu.be/-bfPZG7-MTA

Differential Equations: Electric Circuit: Introduction: https://youtu.be/E6vij-RzQ-o Differential Equations: Direction Fields: Example 1: https://youtu.be/mtbMQQZeMoQ Differential Equations: Direction Fields: https://youtu.be/zWv1y8Xp1ac Differential Equations: General Overview: https://youtu.be/jit59tIY4UI Differential Equations: Spring Motion: Example 1: https://youtu.be/Twu30EJ93Wg Differential Equations: Motion of a Spring: https://youtu.be/mk2TiR5dwVs Differential Equations: Population Growth: https://youtu.be/Td8C_cTEGkA .

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