# Convert discrete formula to continuous formula

• Apr 6th 2013, 03:17 AM
chuackl
Convert discrete formula to continuous formula
By using approximation is it enough proof to show equation left and right is related to each other?

Also, what are the method usually be used to convert equation on right to left?
I have done the question but i would like to see other method as well.
• Apr 6th 2013, 05:32 PM
chiro
Re: Convert discrete formula to continuous formula
Hey chuackl.

What do you mean by related exactly? Do you mean that they are approximately the same?
• Apr 6th 2013, 06:43 PM
chuackl
Re: Convert discrete formula to continuous formula
Yes, if the change is small, both are approximately the same.
However, I would interested to know the way to convert the equation on the right to the left by mean of integration.
• Apr 6th 2013, 06:52 PM
chiro
Re: Convert discrete formula to continuous formula
You need to get something in the form of a summation of f(x)dx or f(x)d(g(x)). If g(x) is continuous, then you get a Riemann Integral but if it is more general (discontinuous for example or not differentiable), then you need to look at the Lebesgue Integral or other similar integrals.

Integrals are just summations involving limits, so once you can get your function into the above form (summing rectangles as the width goes to zero), then you can start to look at the integral form.

To do this you should look at taking your function and expanding it as some kind of Taylor series or equivalent where you get the right summation structure to turn it into an integral.
• Apr 7th 2013, 01:01 AM
chuackl
Re: Convert discrete formula to continuous formula
Thank you for showing the other way of integration.

Please refer attachment in "integration 2" i found that te original equation(linear equation) can be convert from this way to another form of equation.
Just need to substitute P3=P1+dp and V=dv solve for the rest of the equation.

This give me an idea also a discreate equation in 2nd attachment can convert into continuous equation by using the same way as in 1st attachment.

Please verify is this way of doing still obey mathematical rule?
• Apr 8th 2013, 05:27 AM
chuackl
Re: Convert discrete formula to continuous formula
sorry for pushing.

Is the every approach correct and make sense?