Mathcad Plots

One of the most effective methods to view and represent source, temporary, and obtained data is by plotting. To continue comparing Excel and Mathcad started in this chapter, we may say that the first application possesses business and the second scientific plotting. 

In Mathcad, we can create plot via command Graph from Insert menu or via the toolbar of the same name shown in Fig. 6.82. Users can classify Mathcad plots into the following groups  

It is the opinion of the authors that such classificatiOTi is better than given in documentation and references  

There are more plot types than noted above where we listed practically the buttons on the plotting toolbar (see Fig. 6.82) rather than types of plots. Independent group plots (e.g., 2-D Bar plot of graph of errors), are displayed by correspondent formatting of the others, X-Y Plot. 

The authors believe that 3-D plots are rather promotional thing than a method to represent results of large calculations, having practical aims not presentation or advertising, especially, if we should print such plot where we cannot rotate it to see from another point. 

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Constants and variables needed for MathCad plots and computations ... 

We described only two strategies of formatting Mathcad plots (see Figs. 6.91 and 6.93). Nevertheless, there are much more of that especially in 3D plotting. Often the graphs are formatted to transport to books and articles as PrintScreen. In such cases, it is useful to insert the graph created in Mathcad to another application, for example to Paint to finish it off. We have to do that if Mathcad has not necessary formatting tools or they are difficult to access, or we do not know about them. 

Graphical representation and corresponding equations of tabular data are of value for interpolation, for revealing behavior patterns, and other purposes. The most complete software for this purpose is TableCurve. More limited but adequate for the present book are POLYMATH and MathCad. All spreadsheet software, for instance QuattroPro, can make plots of all kinds. In... 

Many software packages, such as PSI-PLOT, Mathcad, and Sigmaplot, can carry out numerical differentiation simply and directly. Also, it is possible to fit the data to a function by the method of least squares and then differentiate. It is best to compare the results of several methods if they agree, one has greater confidence in the results. 

Use Mathcad or some other symbolic algebra program to solve the Ai secular determinant of Table 41-2 in a manner similar to that shown in Fig. 5 for the Bi determinant. Modify the Mathematica commands shown in Fig. 6 to see the square of the I2 harmonic oscillator and Morse wavefunctions and their overlap product for v" = 2 and v = 0, 5, 10, 15, 20, and 25. Obtain plots of these results and discuss the trends that you see. Repeat the exercise for v = 40 and v" = 0, 1, 2, 3, 4, and 5 and note the dramatic intensity variations for the Morse oscillator. Emission from this state, which can be populated by the 520.8-nm krypton ion laser line, is strong to even v" levels but is very weak to odd v" levels (up to about v" = 30). 

The k (retention factor) values are then plotted versus the s pH values, and the inflection point of this sigmoidal relationship could be taken as the sp of that particular compound at particular hydro-organic mixture. The ipKa determined at 30v/v% MeCN was determined to be 3.9 (using nonlinear regression analysis program MathCad 8). This corresponds well to our original estimation of IpKa 3.7. 

Mathcad is a program established to work with formulas, numbers, text, and graphs. Mathcad lets you enter equations expanded fully on your screen. The equation in Mathcad appears the way you might see it on a blackboard or in a reference book. You can even illustrate your work with graphics taken from another Windows application. Mathcad equations can be used to solve any math problem symbolically or numerically, and allows the user to present their work in two and three dimensional plots. 

The plot indicates that the probability of finding the electron in a sphere of radius z is sigmoidal. The trace feature of Mathcad is used to find that with z = 2.66 (r= 2.66 ap) there is a 90.0% probability of finding the electron in the sphere. 

Computations and plots are readily prepared with mathematical software such as Mathcad. 

This is a transcendental equation so it is necessary to solve for A-max with a numerical method, At, may be numerically determined with the numeric solver application of the modern scientific calculator. The Given/Find solve block of Mathcad can be used or a graph containing plots of /(-v) = 1 - a- and g(x) = (I + 2.v)e /T may be prepared. The intercept of/(a ) and g(.r) determines. rmB, Alternatively, expand e-l/v in a Taylor series around. v = 0.4 within the above equation. 

Using the Peng-Robinson equation-of-state programs or MATHCAD worksheets described in Appendix B, we obtain the results in Table 7.5-1. The vapor pressure as a function of temperature is plotted in Fig. 7.5-3. The specific volumes and molar enthalpies and entropies of the coexisting phases have been added as the two-phase envelopes in Figs. 6.4-3, 6.4-4, and 6.4-5.B... 

Analytical solutions and correlation equations are presented rather than graphic results. The availability of many computer algebra systems such as Macsyma, MathCad, Maple, MAT-LAB, and Mathematica, as well as spreadsheets such as Excel and Quattro Pro that provide symbolic, numerical, and plotting capabilities, makes the analytical solutions amenable to quick, accurate computations. All equations and correlations reported in this chapter have been verified in Maple worksheets and Mathematica notebooks. These worksheets and notebooks will be available on my home page on the Internet. Some spreadsheet solutions will also be developed and made available on the Internet. ... 

This relation may be used with equations (B) and (C) to incorporate the change in temperature (and thus the associated reaction rate) with fractional conversion. The present problem can be solved via machine computation by choosing a reaction time sufficient to obtain= 0.97. One may employ a differential equation solver such as those in Mat-lab, MathCad, or other engineering software. With either approach one finds that /a = 0.97 at t = 0.117 h or 7.0 min. Evolution of both the fraction conversion and the temperature of the reaction mixture as functions of time is shown in the two panels of Figure IlO.l. Plots of the dependent variables as functions of the time for the batch reaction... 

Problem 13.22 outlines the use of Mathcad to create an animation showing how contour plots of the H2 LCAO MOs i and < 2 change as R changes. 

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