How do I use 'e'?

Question

How can I apply 'e' to my Calculus formulas and how can I use Euler's Formula? What is Euler's Formula for that matter?

Answer 1

e raised to the power of ( pi times the imaginary number i) will equal -1

e^(π i) + 1 = 0

Eulers equations are often times used to convert trigonometry functions into "more reasonable" equations, given the mathematics involved.

cos x = [ e^(i x) + e^(-i x) ] / 2
sin x = [ e^(i x) - e^(-i x) ] / 2i

They are also used in polar coordinates and the polar form of complex numbers.

e^(i θ) = cos θ + i sin θ

the value "e" can also be used/found in naturally occurring rate-change problems. Many natural events, in physics, as well as in mathematics, exhibit e as a rate of change.

Even in financial mathematics, e is used to compute continuous interest rate problems... as in no compounding intervals but continuous compounding.

In mathematics, when solving for an element using logarithms (including in Calculus) it is often convenient to use base e logs (natural logs) in place of arbitrarily differing base logs.

Answer 2

e is normally used as the base of logarithms. We call such logarithms "Natural Logarithms". They are also called "Napierian logarithms". In these logarithms, the base of the logarithm is the number e. We write them as LN instead of LOG.


For Euler's formula, I recommend you take a look at:

www.planetmath.org

Good luck.

Answer 3

I think you'll find all you need here:

http://en.wikipedia.org/wiki/Euler%27s_formula
http://en.wikipedia.org/wiki/E_%28mathematical_constant%29

Answer 4

This website my be helpful: http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/e.html