What does e represent in calculus and why is it used?

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    Calculus
In summary, e is a number, approximately equal to 2.71828183. It's irrational and transcendental. It has an infinite number of decimals, the first fifteen of which are: 2.718281828459045...
  • #36
So your notion of what a mathematician is differs markedly from some other people's then. LIke I keep saying if I were to label I would label Bohr a physicist. That doesn't a priori exclude him from having made a contribution to mathematics.

Here is a mathematical object:

[tex]\phi(n)[/tex]

a function from N to N, that gives the number of numbers comprime with n between 1 and n. It is called Euler's totient function. Euler was a prolific mathematician and physicist.

Gauss also invented physical theories in astronomy I believe, though don't quote me. The origins of homological algebra lie in studying planetary motion. (hence the apparently disparate meanings of syzygy)

Ah, Dirac, that'd be the dirac who was from Bristol, where I work, as a mathematician, whose portrait hangs in my department? A department which, in a recent report, said that it wished to remove the artificial barriers between the applied and pure world, a department where applied mathematicians study the Riemann hypothesis? Where the applied colloquium two weeks ago was on L-functions and modular forms and where Paul Martin gave a talk aobut statisical mechanics in the pure seminar?


The original point was that although there is no Nobel prize for mathematics, there are prizes won by people who's work has had a strong influence on and been strongly influenced by mathematics, that is all.

The divisions are completely subjective as I believe we have shown here.

jon baez isn't a member of the physics department at UCR, atiyah has contributed abel winning theorems to mathematics that have uses in physics (and last i knew was studying electron distributions), grothendieck is now allegedly studying biology, soem famous category theorist/geometer whose name eludes me isn ow doing computer science, bott was an electrical engineer and mathematician.

The differences are sometimes marked, sometimes fuzzy, but it is all completely subjective, isn't it?
 
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  • #37
Hmm. I wonder, why did you invent natural logarithms. I mean, why don't one just stay to the common ones.
 
  • #38
** perfectly agrees with matt **

Danne,
see here,
http://en.wikipedia.org/wiki/Natural_logarithm

I mean, why don't one just stay to the common ones.
Umm because "e" is more common than any other base.

-- AI
 
  • #39
Hmm. The site states that natural logorithms has rare propertys that are applicable to decays and growth. But doesn't that also include 10-based ones. Ohh, the book I'm reading about this really sucks.
 
  • #40
e occurs naturally in solutions to differential equations.
 
  • #41
Ahh. But when dealing with inverse exponet-problems, the choise between 10-based and e-based is arbitrary, right?
 

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