Calc 1: Differential Calculus

Lecture 5: Exponential and Logarithmic Functions

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This video is about exponential and logarithmic functions. This one is a little long again. I added a little bit at the end about hyperbolic functions. Hyperbolic functions are often neglected, and so I thought it would be worth talking about them a little bit. That did put us over our desired length, though. The hyperbolic functions might seem mysterious, but really they are just combinations of e^x and e^(-x).

You do need to know about hyperbolic functions, because they come up in later classes. What you can probably get away with not worrying about is the inverse hyperbolic functions. Knowing that they exist is probably going to be enough. If we ever need an inverse hyperbolic function (and we might one day!), we can talk about them then.

If you want to learn more about the number e, and why mathematicians think it's such a big deal, you can check out this Numberphile video, where James Grime (from the University of Cambridge) talks about where it comes from. He says he doesn't know why Euler called it "e", but it's because "e" is the first letter in "exponential", or so Euler claimed.