Seriously impressive
This is a shockingly powerful graphing calculator. When you open it, you can chose to define one or two single variable functions, or a parametric curve in Cartesian or polar coordinates, or a function of two variables, or an ordinary differential equation (first or second order). Once you have a function defined, it can graph it along with its derivative-- which it can calculate algebraically. TouchPlot can also calculate a sequence of values for the function, and solve for roots or intersection points. I got a lot more than I was expecting for my $4.99.
Many of the requested features seem to be here (I didnt have the older version). Several reviewers have complained about the interface, but I had no trouble with it at all. The only awkwardness in the function editor comes from not having a parentheses button, but this really is unnecessary. You simply enter the operations in the proper order. For example, (1+2)*3 would be entered by tapping the multiplication button, then addition, and then the numbers 1, 2, and 3. This doesnt take long to get used to.
There are a few imperfections: first, while the function editor includes all the usual elementary functions, floor and ceiling functions, there are no other special functions, like the factorial function, or any special statistics function. You cant save functions you arent using, except by turning their graphs off, which prevents you from putting another function in its place. You can zoom in and out on the graph only by pinching, which makes it difficult to keep the axes on the same scale.
However, the graphs look great, and they can be 3D, with contours, or inequalities-- I still cant get over how much TouchPlot can do, and I still havent explored half of it.
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TouchPlot