What is the upside?

1) You are freed up from the drudgery that takes much time.

2) You can think about the problem without getting sidetracked with the details of solving it.

3) By getting passed things you could not get passed before you now can delve into deeper mathematics because you can use your package to help read journal articles. Incidentally, they do not admit it in the article but most journal articles are now written with the help of a CAS.

4) And this is a big one you never make a careless mistake that blows a solution away. For instance you might have wondered about that faulty solution for many months.

]]>By the way, when you derived that Fourier series for e^x, did you use Mathematica or did you derive it yourself? When I did it myself, I did not appear to get the right answer. Should I post my working?

]]>Now in the plot of e^x and the Fourier series you will not see the orthogonal basis in the plot itself. They are present in the formation of the series.

]]>When we use an orthogonal basis we get this plot. Notice the high angles of intersection.

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