First steps: approximating functions

Last week we played with sines and cosines, and tried to fit them to functions. One thing that we learned for sure is... it's pretty hard! Sometimes we can get a function exactly right, but when we don't, how close is close? We measured this by finding the point of the function that is furtherst away from the approximation. 

Below are two notebooks. This first notebook is the activity that took most of our time last week, play with it again: Finding a mystery function using combinations of sine waves. Open it, and you're off to the races! If you open the notebook in private/incognito mode, you get a clean spate and can start over by re-opening it. You can save your work by using file ---> download. 

The second notebook is about approximating a square wave using sine waves. This is far more complicated, and in fact there is no way to approximate the square wave exactly (why?). We measured how good than by finding the point where the function is furthest from the approximation, but this example will force you to re-think this. 

Remember the question that came up when we met: do we really only need the odd-numbered modes? 

Have fun, and let us know if you have any questions or problems running these notebooks!