My question is this. Is there a math course, or series of courses, that teaches one how to go from a set of scientiffically obtained data to a desciptive function of that data. Example: F=MA, how did newton go from expermentally obtained numbers to this equation. I wish to know how to figure out what operations to preform on the numbers (+,-,*,^,and so forth), how to determine constants, using trig. and hyperbolic operations, ect. It seems that this is important and I was wondering how to do it.
I was only using F=MA as an example, I am more interested in functions as a whole. I have been thinking about the whole concept of graphical analysis. So we take our data plot it, then see what known graph it most closely resembles, and then try to apply a translation or such. My two questions are as follows.
1) What if we can't get a modification of an know function to work, or will all functions fall under some known function.
2) Also, I am currently learning Taylor Polynomials and they made me think of something. If a Taylor Polynomial can fit within most functions and thus mimic it to a good precision. Then lets say we get our experimental data from [a,b]. Then we derive our function, lets say F=MA (for purposes of clairification) Now then we know our function and thus our experimental rule works over [a,b] but what about outside of our tested for set. The function we thought was the law may only be a mimic of our function. I am not positive (I took most of my physics and math 10 years ago) but I believe that F=MA breaks down at the quantum level (is that correct) So how do we know what the boundaries are for given scientific laws, are their boundaries (I have only done basic classes) It seems there should be bounds for scientific rules to be really correct.
Thanks for the info on the courses though.