1) I want to learn how to look at a graph of any function and be able to derive the equation for the function given parameters that are observable. Is this parameterization? Are there any books on how to do this by hand????(adsbygoogle = window.adsbygoogle || []).push({});

2) If the function is too complex to observe and derive, I want to be able to enter parameters into a computer that has an algorithm to make a "best fit" function for the curve. What is this called? What kind of algorithm would a program such as this contain? More particularly, as an example: If a picture is taken of a fast particle in motion on a certain path, how could I derive the function for its position?

Thanks

EDIT: To make it more specific about what I am trying to find out, I think it goes somewhere along the lines of mathematical modeling, parameterization, mutlivariate methods (maybe). Basically I just want to know how to either look at a function and derive it's equation, or make best fits equations for any curve that could represent the path of a particle. Is there a subject centered around deriving functions from observed paths of particles or observable curves in general????

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# Please name this subject and let me know if books are written on it

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