Euler’s formula and Euler’s identity

The video is more than half-way through the calculus coursework, so if you’re unfamiliar with this stuff there’ll probably be some things you don’t understand even if he keeps it simple and don’t go through a more formal proof. The Maclaurin series he’s talking about is just a Taylor series evaluated at x=0, at uni we always call them Taylor series or Taylor expansions but apparently naming conventions differ.

The three videos before that one builds up to this, but if you’re familiar with maths and can remember how to do Taylor expansions and how to deal with trigonometric functions, you should be able to follow this quite easily without watching those as well; I could, as he doesn’t deal with anything here that I haven’t had exams in at a previous point in time. It probably didn’t do any harm that I read 100 pages in Discrete Mathematical Structures this weekend, parts of which contained a brush-up on permutations and factorials (the “!”-thingies in the formulas).

Videos like these were the kind of stuff I had to cut down on a lot during the last month leading up to the exam, those and non-study books. I’m behind on the blogging of the books I’m reading but I’ll get to it.

What do economists learn when taking their education? Most people would probably guess that they/we learn a lot of stuff about markets, industries/firms and some political economy (‘how the economy works’) and such. Maybe something about ‘how to calculate the numbers’. This is another side of the coin. Even though we wouldn’t be asked to go through that proof at an exam, we are (at least some of us) probably expected to know enough math to be able to understand something like this (it depends on the courses). There’s a lot of math and statistics in (some areas of) economics. There’s actually enough to make a guy who voluntarily decides to watch a video like the one above in his spare time think it’s a little too much. Though of course part of the reason why I feel that way is the fact that I suck at math, which is also why I try to get better at it – at least I’m not a math atheist. Now that we are dealing with comics, there’s also this.

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