When it works, the ImplicitPlot function simplifies the generation of the desired pictures. When ImplicitPlot fails to work, you may have to manually turn explicit equations into functions. Needless to say, this can be a difficult process. The function ContourPlot always works for any function of two variables, whether or not ImplicitPlot works. When ImplicitPlot does work, it produces much cleaner pictures.
Many standard applications appear here.
They are divided into related groups of topics. In addition to the fishbowl example, several reviewers liked the error analysis that appears in the discussion of the Shroud of Turin. So the analysis is of a fictional situation. What is remarkable is just how close this fictional study came to the actual study results. You might look at the notebook C-14 Uncertainties that produced the pictures for the Shroud of Turin example because it illustrates how to place multiple functions on a single graph, how to selectively place labelled marks on the axes, how to place a box around a plot, and how to label both axes 3.3 Nonlinear Applications These applications, most of which have variables separable, can be quite tricky to solve using Mathematica.