Mathematics is the language with which God has written the universe. --Galileo.
Centuries of work by scientists since Galileo's time have confirmed his famous sentence. The great Laws of Physics, such as Newton's Laws of Motion, Maxwell's Equations, and the Lorentz Transformations of Relativity, that summarize how physical objects move or interact are mathematical equations, and it is surely not an exaggeration to say that physicists feel most comfortable when they are able to express the results of their experiments in terms of a mathematical expression. Not only is an equation a convenient way to summarize a physical phenomenon, it gives a strong hint of the nature of the order underlying it and guides us to a theory that explains the results.
A goal of research in the physical sciences, then, is to obtain data from an experiment and match it to a mathematical model. This is called "fitting the data". If each data point is a single number (the dependent variable) that depends on another single number (the independent variable), it is possible to plot the dependent variable versus the independent variable to obtain a curve. If we then fit the data, we are "fitting the curve". A simple example of curve fitting is that covered in the beginner tutorial to this tool, namely, the number of counts in a fixed time interval as observed from a radioactive sample as a function of time. Here the elapsed time since the start of the experiment is the x, or independent, variable (the one the experimenter controls since he or she can choose at which times to observe the sample). The number of counts per time interval is then the y, or dependent, variable. A graph of x versus y is an excellent way of displaying the data. One often shows the error bars on the measured y value as well. As the tutorial shows, one may then fit a line or other curve to the data.
Well established mathematical procedures are available for curve fitting, and many software packages are available for download. For example, a very well-known and powerful package is the Markwardt library that runs in IDL. Serious students and professionals will often want to download, install, and use these powerful curve fitting packages. Many internet users, however, may prefer a readily available, easy-to-use online tool for curve fitting. For those users, the present tool is a convenient resource. The interested user uploads data in XML format to the Webnucleo web server. The web server validates the data and then allows the user to view the data in tabular or graphical form. The user can then supply a mathematical expression to attempt a fit of the data and starting guesses for the values of the free parameters. The tool then fits the data using the Markwardt routines, shows the fit parameters and statistics, and allows the user to graph the results.
The best way to start using the tool is to try out the tutorials. Help links in the tool also aid the user in determining the correct input. More background and other related information is available from the Papers & Links sidebar link. We hope you enjoy the tool, and, as always, we welcome feedback.
