## Solution: epsilon proof: lim 0.9999...=1

Posted Jul20-12 at 02:03 PM by John Creighto
Updated Jul20-12 at 06:19 PM by John Creighto

In another form I presented a proof (post #145)that the lim of 0.9999....=1 using epsilon delta arguments. I was asked to explain each step so I am moving it here for the latex support.

Quote:
0.999... + 0.1 = 1 + 0.099...
0.999... + 0.01 = 1 + 0.0099...
0.999... + 0.001 = 1 + 0.00099..
I do not prove this but it follow from basic arithmetic (by the way numbers carry in addition)....
Posted in Uncategorized

## Laplace Transform Via Limits

Posted Jul14-12 at 02:23 PM by John Creighto
Updated Jul14-12 at 06:24 PM by John Creighto

Quite a while back I had a brief interest in wheather the Laplace transform made numerical sense. I was interested in this for its own sake:

Laplace Transform Convergence
Laplace Transform (Numeric Computation?)

and because if we could numericaly understand the Laplace transform it might tell us more about a dynamic system then a fourier transform.

using the fft to calculate the laplace transform

Memory of my failures in obtaining...
Posted in Uncategorized

## Approximating Non Linear Systems by Using The Matrix Eponential

Posted Jul17-09 at 10:39 PM by John Creighto

For simplicity let's consider a very simple ODE.

$$\dot{x_1}=a x_1^2$$

We can approximate this first order system with a second order ODE as follows:

[tex]\left[ \begin{array}{c}
\dot{x_1} \\
\dot{x_2} \end{array} \right]
=
\left[ \begin{array}{ccc}
0 & 1) \\
0 &
\frac{d f(x_1)}{d x_1}
\end{array} \right]

\left[ \begin{array}{c}
X_1) \\
X_2 \end{array}...
Posted in Uncategorized