hexsol

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These are questions asked by hexsol

Hi!

So I like to check that my manual integrations and/or maple integrations are equal with each other. I normally do this using the Test Relation function.

I was working on a problem and noticed that Maple didn't evaluate the integrals being the same, even though they presumedly are.

Could anyone shed some light on why I get this inequality?

Thanks in advance!

mapleintvsmanualint.mw

restartNULL

dn/dt = -r__S*V

 

We can define n as C*V 

dC*V/dt = -r__S*V

 

We can define the concentration C as S  

dS/dt = -r__S

 

where -r__S = V__max*[S]/(1+K__1*[S]+K__2*[S^2])

  

ds/dt = -V__max*[S]/(1+K__1*[S]+K__2*[S^2])=

 

1/dt = -V__max*[S]/((1+K__1*[S]+K__2*[S^2])*ds)

 

dt = (1+k__1*[S]+K__2*[S^2])*ds/(V__max*[S])

 

"ⅆt = 1/(`V__max`*[S])+`k__1`/(`V__max`)+(`K__2`*[S])/(`V__max`)*ⅆs"

 

int(1/(V__max*S)+K__1/V__max+K__2*S/V__max, S = S .. S__0)

 

`assuming`([simplify(combine*(int(1/(V__max*S)+K__1/V__max+K__2*S/V__max, S = S__ .. S__0)), size)], [S > 0, S__0 > S__])

combine*piecewise(And(0 < S__0, S__ < 0), undefined, (1/2)*(K__2*S__0^2-K__2*S__^2+2*S__0*K__1-2*K__1*S__+2*ln(S__0)-2*ln(S__))/V__max)

(1)

 

`assuming`([simplify(int(1/(V__max*S)+K__1/V__max+K__2*S/V__max, S = S__ .. S__0), size)], [S > 0, S__0 > S__])
  piecewise(And(0 < S__0, S__ < 0), undefined, (1/2)*(K__2*S__0^2-K__2*S__^2+2*S__0*K__1-2*K__1*S__+2*ln(S__0)-2*ln(S__))/V__max)NULL

 

 

maple*equation = manual*equation  NULL

(S__0^2*K__2-K__2*S^2+2*S__0*K__1-2*K__1*S+2*ln(S__0)-2*ln(S))/(2*V__max) = (ln(S__0/S)+K__1*(S__0-S)+(1/2)*(-S^2+S__0^2)*K__2)/V__max"(->)"false

   

eq1 := (S__0^2*K__2-K__2*S^2+2*S__0*K__1-2*K__1*S+2*ln(S__0)-2*ln(S))/(2*V__max)

 

eq2 := (ln(S__0/S)+K__1*(S__0-S)+(1/2)*(-S^2+S__0^2)*K__2)/V__max

 

eq1-eq2 = 0"(->)"false

 

(ln(S__0/S)+K__1*(S__0-S)+(1/2)*(-S^2+S__0^2)*K__2)/V__max = (ln(S__0/S)+K__1*(S__0-S)+(1/2)*(-S^2+S__0^2)*K__2)/V__max

 

Download mapleintvsmanualint.mw

Hi!

I am working on a chemical engineering problem and trying to find a value (Ua) that does not result in a reactor temperature (T) exceeding 398.15 K.

I am employing a system of ode's, secondary functions, variables, starting conditions etc., and the dsolve function to determine these parameters.

Some values are given or calculated, UA is not. So for now I have just been guessing at the value (needed to preform the dsolve initially) and plotting to see relations to T and other parameters. My teacher has directed us to employ this trial and error apporach, which I find time consuming.

There is of course a smarter, more time efficient way of doing this and I was wondering how one could implement this? Moreover, how does one find the values of all the other variables at this Ua value? Is there a one-liner?

I tried implementing a loop to check for max UA values <= 398.15, but was not able to implement it..

Any help would be kindly appreciated.

FindingExtractingvaluesdsolvewithspecificconditions.mw

Hey!

I am having difficulties inputting in text and math mode in my Maple 2023 document. It was working fine in the beginning, but all of a sudden the problem occured. I was restarting maple initially which would temporarily solve the problem, now I cannot input anything after restart. I am doing exam excercises and have been copy/pasting text from a pdf into the document. 

I have tried to install Maple 2024 and open the file but to no avail.  Any help/ pointers would be greatly appreciated.

The attached file -

ml.mw

Hi

I was wondering how one uses maple to solve for variables that comprise the limits of an integral?

X and R are between 0 and 1.

Any thoughts would be greatly appreciated, thanks in advance...!

Download Solvingforlimitsofintegrals.mw

Hi

I found the Manipulate Equation command tool in Maple and was wondering whether it could help me rearrange my equations into giving me certain quotient? One can do it by hand, but at an exam, time saved makes a difference and one can make silly mistakes. The math rearangement is also rather trivial...

Download rearrangemanipulate.mw

Any thoughts would be greatly appreciated, thanks in advance..!

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