Thread: Can anyone explain the concept of mathematical e in simple words?

I just dont understand the explanations on the web and they're so complicated.

It's the constant you use to count the money you should receive when you put your money in the bank. That way you can know which bank is cheating you.

If you want to know how, use the formula Pe^(rt), where P is your premium (starting money), e is the constant, r is the p.a. rate, and t is the time in years.

So let's say I put in 1 dollar for 1 year in a bank with 100% p.a. (not possible, but it is in wonderland :]). I just plonk in 1*e^(1*1), which roughly comes to 2.72. So in 1 year you earn 1.72 dollars. When you realise you get only 2.70 dollars, then it's time to change bank because it's cheating your 2 cents. >:[

That's just one of the useful things it can do. The rest are complicated. (Or so.)

"e" is called the Napaerian constant or Euler's constant. It is irrational and has the first few digits as 2.71828..................

It is the base of Natural Logarithm (ln function). "e" is used in engineering calculations, Calculus, and complex numbers. Its precise numbers are obtained by infinite series (Taylor Series).

Looking at Calculus, d/dx (ln x) = 1/x and d/dx (e^x) = e^x. These results exhibits the peculiarity and beauty of this special number.

In complex numbers, e^(ix) = cos x + i sin x ---------> Euler's formula.

With this we get the results of complex trigo expansion like cos (3x) and sin (3x)and so on.

So appreciate the beauty of this number, e.

Regards
Edem

e = 0

as in "eeeeewww there is no way I'm gonna read all these other lame responses"

e has been chosen because it is convenient for calculus.

It is the one number where, if

y = e^x

then
dy/dx = e^x

In English, this means that if you draw the curve y = e^x on a graph and go to the point on the curve where y=3 the slope will be 3, if you go to the point where y=99 the slope will be 99, in fact where ever you are on the curve, the value of y is the same as the slope (because they are both equal to e^x). To put it in one sentence;

The value of e^x is always equal to its slope.

There is only one number for which this is true and it is e.

see graph http://content.tutorvista.com/maths/content/us/class11maths/chapter17/images/img40.gif

Out of interest, note that this means e^x is it at 45 degrees when y=1 and this is at an x value of zero (1=e^0).

Also e^x is horizontal (dy/dx = 0) at y=0 but this only happens at x = -infinity

The reason that it is handy is that once you have worked out what e is, it becomes possible to do calculus on any number to the power of x because we can express the problem in terms of e and we already have an easy answer for that bit.

You will also discover that any growth or decay equation, where the rate of growth is proportional to the current value, can be expressed in terms of e and through the rules of indices it turns into e^(ax) which is nice and easy for calculus.

the whole WORLD has been basically built on the MATH .....
and the great Mathematician is certainly GOD....
cause anything in the world are considered according to the sizes and amounts by GOD ...