I haven't worked with partial derivatives since high school 25 years ago so I'm quite a bit rusty and need a little guidance. I'm reading through a paper and would like to write a program to simulate it. The equations are:(adsbygoogle = window.adsbygoogle || []).push({});

Eq 1. Eq 13. M=f*Po+f*(Pb-Po)*(1-ln(e)^(-0.693*time/Halftime)

Eq 10. a=3.25*Halftime^-0.25

Eq 11. Mo=152.7*Halftime^-0.25

Eq 12. D=(M-Mo)/a

Eq 13. D=(f*Po+f*(Pb-Po)*(1-ln(e)^(-0.693*time/Halftime)-Mo)/a

Where:

f= gas fraction

Po= initial pressure

Pb= bottom pressure

I'm having problems setting up equation 13 where:

"The partial derivative of Eq 13 with respect to Halftime is the rate of change of hte decompression stop depth with respect to the tissue halftime for any bottom time(time), depth(Pb), and M value. When this partial derivative equals zero, the stop depth is minimumized and we get the Halftime of hte deepest stop depth. When we substitute the critical halftime value in Eq 13 we get the deepest stop depth."

So Halftime can be expressed as a function of time, but I can not figure out where to get to this point. I can post a link to the paper if anyone needs further clarification.

Any help would be greatly appreciated!

Thank you,

Rob

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# PDE help needed setting up the equation

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