University students in engineering often have assignments in which they must show their work step-by-step with sample calculations. Although Excel and Python are useful for advanced calculations, they can't present complex equations formally in a report.

MathCAD [1] is a good package for writing engineering reports. The tool offers a workbook interface that allows you to enter complex equations in a readable format, along with a rich function library, programming interface, graphics, and plots. Unfortunately, MathCAD isn't supported in Linux, and it is generally out of the budget for students or casual users. As an alternative, SMath is a great free option that works in Linux, macOS, and Windows.

In this article I introduce SMath and show you some of the useful features that I expect to use in my next engineering term. I also look at an SMath example that solves a typical high school or first-year university math problem.

Getting Started

The SMath installation files reside on the project's website [2]. To install the software, the Mono development environment needs to be loaded first. In Debian/Raspbian/Ubuntu systems, enter:

sudo apt install mono-devel

In the next step, copy the SMath installation files to a local directory on your laptop and run the SMath desktop:

# run SMath Studio in Linux:
./smathstudio_desktop_mono

SMath Studio has a side panel of common functions and symbols (Figure 1). All the functions are listed in the Insert Function (fx) dialog box.

Equations, Variables, and Units

SMath lets you create complex calculations from the side panel (Figure 1) or with keyboard shortcuts. Complex equations can be modified with the arrow keys to move the cursor between elements (Figure 2).

Figure 1: Panel of common functions.

Figure 2: Editing and viewing a calculation.

SMath Sheets calculate from top left to bottom right, so it is important to define a variable before it is used. A variable is defined with :=, and the results of a calculated value are displayed with the equals sign (=).

To add units to a variable, type a single quote (') before entering the unit, or you can choose from a list of units (Figure 3). If a calculation has mixed units, SMath automatically manages the conversion between units (Figure 4).

Figure 3: Inserting units.

Figure 4: Mixing units.

To make things a little more presentable, SMath shows variables, calculations, and results in black and units in blue, although this feature is adjustable. The final results of a calculation can be presented in fractions, unit conversions, or simply the numeric value.

Solutions

SMath also supports useful features such as interface widgets and plotting, as well as conditional code. One problem that regularly needs to be solved in high school and many first-year university courses is to find x intercepts and the area under a parabola defined by a quadratic equation. The next example solves this problem and highlights some of the key features built into SMath.

The first step in solving this problem is to define the input variables. User interfaces such as adjustable sliders can be added from the Insert menu in the toolbar (Figure 5). Slider widgets define and toggle variables (Figure 6).

Figure 5: Inserting a slider.

Figure 6: Defining variables with interface widgets.

Plotting a parabola is a quick way to check the number of x intercepts for an equation. To add a plot, use Insert | Plot | 2D (Figure 7). Once a plot is dropped onto a workbook it can be resized and repositioned. For this example, the plot is configured to show the f(x) quadratic equation.

Figure 7: Inserting a plot.

You can quantitatively find the number of x intercepts in two ways (Figure 8): by manually solving the quadratic formula for x when y=0, or with the SMath solve(2) function. To insert this function, type solve, then press the Tab key once the dropdown menu displays solve(2). To find the area under the curve, the results of the solve function should be defined as a new variable (e.g., MyRoots).

Figure 8: Finding x intercepts.

The solve(2) function returns one or two x intercepts where the curve touches or crosses the x-axis. If you don't change your settings to Calculation | On error | Continue (Figure 9), the logic will be interrupted if a curve does not cross the x-axis.

Figure 9: Changing calculation settings.

Added logic can handle special cases. To solve for the area under the curve, I used the if statement then checked for valid roots (Figure 10). An IsDefined function checks whether the MyRoots variable is valid (i.e., has roots).

Figure 10: How to insert conditional code.

If roots are found, the limits are passed to an integral function to calculate the area. (Integral and derivative functions are found in the Functions side panel.) If no roots are found, the string "Equation doesn't cross axis" is passed to the area variable.

Figure 11 shows the final SMath worksheet example, with the interface widgets and plotting and conditional code that find the x intercepts and area under a parabola with the quadratic equation.

Figure 11: Slider, plot, and code example.