can anyone , provide me, the mathematical equation of the curve life ? any references, documentations, thanks in advance.
Hi Ali,
There are many examples. Here are just a few:
Example #1: Drug Dosage
In prescribing drug dosage, physicians know that residual buildup depends on the time interval between administration of drug doses. They use sub-models for decay rate, assimilation rate and drug concentration with repeated equal doses for prescribing a safe and effective dosage of drug concentration and dose schedule.
Example #2: Time of Death
At the beginning of a murder investigation, a forensic pathologist will go out into the field to examine the scene and then uses Newton's Law of Cooling to approximately determine a victim's time of death.
Example #3: Reactor Risk Assessment
A process operator uses ODEs to analyze the transient response of a reactor in a manufacturing plant (i.e., petrochemical, semiconductor, pharmaceutical) to ensure that it is safe for continuous production without interruption.
Frankly, all the models are hidden! But they are everywhere and permanently! Every car accelerates according to the second order ODE, the level of the water in rivers changes according to ODE, cooling a drink with the use of ice is governed approximately by some first order ODE, same - when cooling a warm drink without ice:), emptying a wash machine can be described by some ODE - which allows to predict the time needed for this "process", drying painted floor is also described by such equations. The every-day user sees only the intruction(s), but they are formulated on the basis of calculations - some of which are solutions to ODE.
Regards, Joachim
Thank Mr, Yew-Chung Chak , Yew-Chung Chak , for your answers, they were very helpful for me, if I want to better understand the theme what are the basic references that you can advise me ?
Hi Ali,
You will find lots of examples in the undergraduate textbooks on Differential Equations:
- Differential Equations: An Introduction to Modern Methods and Applications, 3e
- Differential Equations: Computing and Modeling, 5e
- Fundamentals of Differential Equations, 9e
- A First Course in Differential Equations with Modeling Applications, 11e
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