Isn't calculus only as useful and accurate as the function itself?

Question

That is, how do engineers apply calculus to experimentally derived functions? How does an enginner know that a function applies to the specified range of the phenomena in question?

Granted, I realize the universal law of gravitation
(a=9.8m/(s^2)) is set in stone, but how do engineers apply calculus when calculus demands the sample of analysis to be an accurately defined function?

Answer 1

If there is no accurately-defined function for the behavior of some system, you experiment, plot your data, and try to find a function that fits the data.

If the governing function is known, but not solvable in closed form (for example, turbulent fluid flow), you use numerical techniques and approximate a solution by numerical integration and iteration.

For example, the Gaussian shape
f(x) = e^(-x^2)
cannot be integrated analytically. It can, however, be integrated numerically, yielding useful results.

Answer 2

Hey we set limits and ranges and avoid the extrema. Its not as cut and dry as you might think. Lets say we need an electric motor that will do 9 hp constantly (sf 1.0) do you think we spec out a 9hp motor ? Heck no we get a good 12 hp at sf .85 and let her rip. Sometime the exact approach is not a good as the data says it is. Oh yea we could sit around and set up a curve for a pump that looks like a smooth tangent line till infinity was reached but by then the job at hand has passed us by. Remember the significant figure problems you have had. Adjust your life to the least significant digit adjust your schoolwork to the teachers request. Calculus grants us the crystal ball to project a view of events that have not happened onto a plane(the paper or whatever) so we can conceive a plan that will work for the worst cases. In closing only disciple will allow yourself to be confined by relative amounts . Sometimes you have to step up and make that leap of faith and the analysis you speak of is your support for just that moment.
Go get em ... I liked your Question by the way!! Good luck from the E!!!

Answer 3

This is what experimtation is for.