UltimaCalc Professional

UltimaCalc is a collection of mathematical tools wrapped up in one program, for use by scientists, engineers and students. The main window is a calculator that accepts mathematical expressions as plain text and evaluates them to 38 digit precision.
UltimaCalc can remain always ready for use. The use of text input means that this window can be small enough to remain open at all times without blocking the view of other windows. This window can be partially transparent when inactive, so you can read documents open underneath it.
A major feature of UltimaCalc Professional is its Symbolic Algebra module: Simplify expressions, differentiate them. Integrate a wide range of expressions, and see how the result was obtained. Find Taylor series. Factorise polynomials, divide one polynomial by another or find their GCDs.
Analyse a set of measurements, or approximate complicated functions with simpler ones. Use a variety of methods to fit lines to data, plotting the result. Calculate linear regression, or use an absolute deviation fit to minimise the distorting effects of outliers. Perform a multivariate linear regression when one variable is a linear function of several others. Fit polynomials and other non-linear expressions to the data.
The Standard Deviation tool calculates the mean, median, standard deviation, skewness, etc of a data set.
Other tools solve simultaneous linear or non-linear equations; find the values of parameters that minimise the value of an arbitrary expression; find roots of polynomials up to tenth order; or solve triangles.
Plot arbitrary functions. Specify starting and ending conditions and how variables X and Y change at each step. Combine up to 8 plots.
Save your results: the calculator window and most special tools can record all calculations in a plain text file. Most special tools can also save their data along with notes to a calculation file future reference. All graphs and plots can be saved as image files in a variety of formats.