Graphing Functions and Expressions / 119
Graphing Functions and Expressions
2D QuickPlots
A 2D QuickPlot is a plot created from an expression or function that represents the y- coordinates of the plot. Mathcad automatically creates a plot over a default domain for the independent variable, from –10 to 10 for an X-Y plot and 0° to 360° for a polar plot.
To create an X-Y QuickPlot of a single expression or function:
1.Type the expression or function of a single variable you want to plot. Click in the expression.
2.Choose Graph > X-Y Plot from the Insert menu.
3.Click outside the graph or press [Enter].
To change the default domain for the independent variable in a 2D QuickPlot, change the axis limits on the plot.
Defining an Independent Variable
You can set your own range by defining the independent variable as a range variable before creating the plot:
1.Define a range variable. See “Range Variables” on page 84.
2.Enter the expression or function you want to plot using that variable. Click in the expression.
3.Choose Graph > X-Y Plot from the Insert menu.
4.Type the name of the variable into the x- axis placeholder.
5.Click outside the graph or press [Enter].
Mathcad plots one point for every value of the range variable, and unless you specify otherwise, connects each pair of points with a straight line. To smooth out the curve, make the step size of the range variable smaller.
120 / Chapter 11 2D Plots
Plotting Multiple 2D Curves
You can graph several traces on the same X-Y or polar plot. A graph can show several y-axis (or radial) expressions against the same x-axis (or angular) expression. See Figure 11-3. Or it can match up several y-axis (or radial) expressions with the corresponding number of x-axis (or angular) expressions. See Figure 11-2.
To create a QuickPlot containing more than one trace:
1.Enter the expressions or functions of a single variable you want to plot, separated by commas.
2.Click in the expressions, then choose Graph > X-Y Plot from the Insert menu.
3.Click outside the graph or press [Enter].
In a QuickPlot with multiple traces, you need not use the same independent variable in every y-axis (or radial-axis) expression. Mathcad provides the appropriate corresponding variable in the x-axis (or angular-axis) placeholder.
To create a graph containing several independent curves:
1.Choose Graph > X-Y Plot from the Insert menu.
2.Enter two or more expressions separated by commas in the y-axis placeholder.
3.Enter the same number of expressions separated by commas in the x-axis placeholder.
If you specify more than one independent variable, Mathcad matches up the expressions in pairs — the first x-axis expression with first y-axis expression, the second with the second, and so on. It then draws a trace for each pair. Figure 11-2 shows an example.
Figure 11-2: Graph with multiple expressions on both axes.
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Figure 11-3: Graph with multiple y-axis expressions.
Note All traces on a graph share the same axis limits. For each axis, all expressions and limits on that axis must have compatible units.
Creating a Parametric Plot
A parametric plot is one in which a function or expression is plotted against another function or expression with the same independent variable. You can create either an X-Y or polar parametric plot.
To create an X-Y parametric plot:
1.Choose Graph > X-Y Plot from the Insert menu.
2.In both the x-axis and y-axis placeholders, enter a function or expression.
3.Press [Enter].
Mathcad produces a QuickPlot over a default range for the independent variable. Figure 11-1 shows an example of a parametric plot.
If you don’t want Mathcad to use a default range for the plot, define the independent variable as a range variable before creating the plot. Mathcad plots one point for each value of the independent variable and connects each pair of points with a straight line. Figure 11-4 shows two functions of θ plotted against each other. The range variable θ was previously defined. See “Range Variables” on page 84.