Euler's method
Euler's Method is a tool that helps us estimate the value of something that is changing over time. Let's say you are trying to measure the temperature outside. The temperature changes slowly over time and you can measure it at different times. Euler's Method can help you estimate what the temperature will be at a future time based on the measurements you've already taken.
Here's how it works:
Imagine you are on a bike and you start at one point and want to end up at another point. But you can only bike a certain distance in one push. So you bike a little bit and see where that gets you. Then you bike a little bit more and see where that gets you. You keep repeating this process until you get to your destination.
Euler's Method works in a similar way. Instead of biking, we use math! We take an initial guess of what the value will be at a certain time, and then we use some math formulas to estimate what the value will be at a later time. Then we repeat this process to get closer and closer to the actual value.
Let's go back to the temperature example. If we measure the temperature at 10AM and it's 20 degrees Celsius, and we know that the rate at which the temperature is changing is 1 degree Celsius per hour. We can use Euler's Method to estimate what the temperature will be at 2PM.
We first take our initial value of 20 degrees Celsius at 10AM, then we use our formula to estimate what the temperature would be at 11AM, then 12PM, and so on until we reach 2PM.
By using Euler's Method, we may not get an exact value of the temperature at 2PM, but it gives us a good estimation based on the information we have.
Overall, Euler's Method is a helpful tool that uses math formulas to estimate how something changes over time based on initial values.
Here's how it works:
Imagine you are on a bike and you start at one point and want to end up at another point. But you can only bike a certain distance in one push. So you bike a little bit and see where that gets you. Then you bike a little bit more and see where that gets you. You keep repeating this process until you get to your destination.
Euler's Method works in a similar way. Instead of biking, we use math! We take an initial guess of what the value will be at a certain time, and then we use some math formulas to estimate what the value will be at a later time. Then we repeat this process to get closer and closer to the actual value.
Let's go back to the temperature example. If we measure the temperature at 10AM and it's 20 degrees Celsius, and we know that the rate at which the temperature is changing is 1 degree Celsius per hour. We can use Euler's Method to estimate what the temperature will be at 2PM.
We first take our initial value of 20 degrees Celsius at 10AM, then we use our formula to estimate what the temperature would be at 11AM, then 12PM, and so on until we reach 2PM.
By using Euler's Method, we may not get an exact value of the temperature at 2PM, but it gives us a good estimation based on the information we have.
Overall, Euler's Method is a helpful tool that uses math formulas to estimate how something changes over time based on initial values.