1. Symbolic Algebra
Algebraic expressions manipulated with ease. Multiply out complicated expressions, simplify them. Do calculus. Find an integral and see how it was found. Obtain Taylor series. Find the greatest common divisor of two polynomials. Convert trig expressions to different forms. Factorise polynomials. Calculate with integers to thousands of digits.
2. Standard Deviation
Estimate the variation about its average of a set of data. Calculate the mean, median, sample standard deviation and population standard deviation of the data. Also the variance, skewness and coefficient of kurtosis.
3. Regression and Least Squares Fit
Estimate trends in data, or fit data to a curve. UltimaCalc performs the usual least squares linear regression, and also does least squares polynomial fitting, multivariate regression, and absolute deviation regression.
Given a nonlinear expression with a set of variables, you can calculate the values of the variables that optimise the fitting of the data to the expression.
You can view a plot of the result and save this as an image file in various formats.
4. Simultaneous Linear Equations
Solve problems such as: If two widgets, a grommet and a trunnion cost $15, three widgets two grommets and a trunnion cost $22, and one widget, three grommets and two trunnions cost $25, how much does a single trunnion cost? (Assume that you do not get a quantity discount!)
5. Simultaneous Non-linear Equations
Solve an arbitrary equation containing one unknown. For what values of
sin(x)/x=0.1? Solve more complex problems such as: Given two arbitrary curves, do they intersect, and if so, where? Solve
N non-linear equations in
6. Minimise / Optimise
Given an expression containing variables, find the values of the variables that minimise the values of the expression. This is conceptually similar to finding the lowest point in mountainous terrain, except that you are not restricted to only two horizontal dimensions. This can also be seen as optimising the expression.
7. Plot Functions
Plot up to eight functions at a time, viewing them individually or all together. You have full control over how the plotting is done, and can save the plot as an image file in various formats.
8. Polynomial Roots Calculator
Calculate the real roots of polynomials. This polynomial root calculator complements the ability to factorise polynomials in the Algebra module. The real roots of a polynomial are usually irrational numbers, whereas the polynomial factorisation method in Algebra only finds polynomial roots that are real rational numbers.
9. Solve Triangles
Given three facts about a triangle (one of which must be the length of a side, and the others must be sides or angles), UltimaCalc will calculate the solution of the triangle. This means calculating the unknown sides, angles, area and perimeter. UltimaCalc also provides a visual display of the triangle.
10. Create Charts
Display data to its best advantage. Choose the most suitable kind of chart: a bar chart, stacked bar chart, or pie chart (all in either 2D or 3D), a line chart or a ribbon chart. Add a title, subtitle, and explanatory legend. Arrange the layout of all these elements, and save the result as an image file which you can include in a Word document or some other kind of report.
Given the latitude and longitude of two places, UltimaCalc will calculate the Great Circle and Rhumb Line routes between these two places.