I’m going through MIT’s 18.01 course on OCW to prep for the 18.01 ASE which I’m hoping to take in August. The content is great but the organisation on the website isn’t. I’m currently writing up what I hope is an improved version, but I digress.
In the Graphing Functions Notes
odd functions are mentioned:
→ An even function is one whose graph is symmetric with respect to the y-axis:
→ An odd function is one whose graph is symmetric with respect to the origin:
What’s neat is that every function can be written as the sum of an
even function and an
odd function where:
Now, I only found this out while trying to do the first off the Problem Set questions, which I’ll show a solution for below. But first the proof
Suppose that the statement was true.
Let where e is even and o is odd
but we know that and so:
Now, we just have to show that is
odd and we have proved this
and this is an odd function: