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Figure from:Curve Graphing in MS Excel and Applications

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3.2.2. Second Method

Figure 6 3.2.2. Second Method

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For instance, if a = 0 and b = 2, the implementation of the above steps will yield ne results shown in Figure 2.
For instance, if a = 0 and b = 2, the implementation of the above steps will yield ne results shown in Figure 2.
We will use the above method to implement a zooming technique later.
We will use the above method to implement a zooming technique later.
Figure 5: The plotted sine function
Figure 5: The plotted sine function
Figure 8: The dialog box to paste a second graph latter graph on the same chart, select the range of x-y points for the graph, point to
Figure 8: The dialog box to paste a second graph latter graph on the same chart, select the range of x-y points for the graph, point to
Figure 10: Plot of the functions e* — 2x’ (left) xsin(10x) (right) Graphs of curves that do not represent functions
Figure 10: Plot of the functions e* — 2x’ (left) xsin(10x) (right) Graphs of curves that do not represent functions
Figure 12: Filling the gap in the graph CURVE GRAPHING IN MS EXCEL AND APPLICATIONS Parametric and Polar curves Parametric and polar curves pose no special challenge to Excel graphing. In the case of a parametric curve (X = f(t), y=g (t)), an extra column for the values of t is needed. The values of x and y are then generated using the functions f andg. Fora polar curve (Tf = £(0) ), a column of values of @ is first generated, a corresponding column of the values of r is then computed. The x and y values are generated using the formulas xX =rcos@, y =rsin@. Figure 13 shows parts of Excel tables for the cycloid x =t—sint, y =1—cost and the butterfly curve r =e’ —2cos40+sin’ 0/4 (21. needed. The values of x and y are then generated using the functions I andg. Fora
Figure 12: Filling the gap in the graph CURVE GRAPHING IN MS EXCEL AND APPLICATIONS Parametric and Polar curves Parametric and polar curves pose no special challenge to Excel graphing. In the case of a parametric curve (X = f(t), y=g (t)), an extra column for the values of t is needed. The values of x and y are then generated using the functions f andg. Fora polar curve (Tf = £(0) ), a column of values of @ is first generated, a corresponding column of the values of r is then computed. The x and y values are generated using the formulas xX =rcos@, y =rsin@. Figure 13 shows parts of Excel tables for the cycloid x =t—sint, y =1—cost and the butterfly curve r =e’ —2cos40+sin’ 0/4 (21. needed. The values of x and y are then generated using the functions I andg. Fora
Figure 14: Two loops of a cycloid
Figure 14: Two loops of a cycloid
Excel graphing is also a great tool to study the dependence of graphs on parameters. We illustrate this by plotting the graph of the polar curve f=a+cosé for various values of a. The table set up is the same as the one for polar curves except that we need an extra cell to store the value of a. The lay out of the table is shown in Figure 16. Figure 16: Table for the curve f =a +COSO@
Excel graphing is also a great tool to study the dependence of graphs on parameters. We illustrate this by plotting the graph of the polar curve f=a+cosé for various values of a. The table set up is the same as the one for polar curves except that we need an extra cell to store the value of a. The lay out of the table is shown in Figure 16. Figure 16: Table for the curve f =a +COSO@
CURVE GRAPHING IN MS EXCEL AND APPLICATIONS The values of the parameters can also be controlled by scroll bars. Figure 18 shows an implementation of this idea. In this figure, cells A2, B2, C2 and D2 are named as cont (for counter), a, theta and r_, respectively. The scroll bar implementation is done as follows:
CURVE GRAPHING IN MS EXCEL AND APPLICATIONS The values of the parameters can also be controlled by scroll bars. Figure 18 shows an implementation of this idea. In this figure, cells A2, B2, C2 and D2 are named as cont (for counter), a, theta and r_, respectively. The scroll bar implementation is done as follows:
One thing to notice in Figure 18 (and also in Figure 17) is that the correct value of the parameter always shows in the chart title. To do this automatically, insert a Text Box from the Drawing Toolbar, click inside the text box to activate it and type the formula =a in the formula bar. When you press enter the current value in the cell named a (B2) will be displayed in the text box.
One thing to notice in Figure 18 (and also in Figure 17) is that the correct value of the parameter always shows in the chart title. To do this automatically, insert a Text Box from the Drawing Toolbar, click inside the text box to activate it and type the formula =a in the formula bar. When you press enter the current value in the cell named a (B2) will be displayed in the text box.
by plotting the function over the interval |— 3,5] as shown in Figure 19. Figure 19: The polynomial plotted on a “large” interval Suppose we want to find the roots of the equation x° —4x* +3x-10=0. One way to do so is to plot the graph over a large range and then zoom in on the roots, one by one, to better bracket them. For this purpose we use the technique for generating values in an interval [a,b] that was explained in Section 2.2. We started by plotting the function over the interval [_ 35] as shown in Figure 19.
by plotting the function over the interval |— 3,5] as shown in Figure 19. Figure 19: The polynomial plotted on a “large” interval Suppose we want to find the roots of the equation x° —4x* +3x-10=0. One way to do so is to plot the graph over a large range and then zoom in on the roots, one by one, to better bracket them. For this purpose we use the technique for generating values in an interval [a,b] that was explained in Section 2.2. We started by plotting the function over the interval [_ 35] as shown in Figure 19.
At this point, by looking at the table of generated y-values we see that the root is actually between 3.992 and 3.995. This means we have bracketed the root to two decimal places. Observe also that if you move the cursor near the root, the yellow hint box will appear giving the following points:
At this point, by looking at the table of generated y-values we see that the root is actually between 3.992 and 3.995. This means we have bracketed the root to two decimal places. Observe also that if you move the cursor near the root, the yellow hint box will appear giving the following points:
Table 1: Data for online graphing/analysis
Table 1: Data for online graphing/analysis
Figure 22: Step 1 of the Text Import Wizard respectively. In C2 enter the formula =Shear/Stress (do not worry about the error message that appears when you press Enter). The ratios generated in Column C represent analysis that we want to perform on the generated data. Select cell A2 and then click Data, Import External Data, Import Data... to open the Select Data Source dialog box. Navigate to where you saved the dat.txt file (My Documents in this example), select the file and then click Open to bring up the Text Import Wizard shown in Figure 22: Step 1 of the Text Import Wizard.
Figure 22: Step 1 of the Text Import Wizard respectively. In C2 enter the formula =Shear/Stress (do not worry about the error message that appears when you press Enter). The ratios generated in Column C represent analysis that we want to perform on the generated data. Select cell A2 and then click Data, Import External Data, Import Data... to open the Select Data Source dialog box. Navigate to where you saved the dat.txt file (My Documents in this example), select the file and then click Open to bring up the Text Import Wizard shown in Figure 22: Step 1 of the Text Import Wizard.
Now with the range A1:C4 generate the two graphs shown in Figure 26.
Now with the range A1:C4 generate the two graphs shown in Figure 26.
Figure 27: More data imported, analyzed and plotted
Figure 27: More data imported, analyzed and plotted