Polymath Software

Fit a set of experimental data using the regression option using the REG option. 

Consider the following reaction taking place in a batch reactor  

POLYMATH 6.0 Educational Release - [Ordinary Differ ential Equations Solver] 

I File Program Edit Format Problem Examples Window Help 

I SoivB system ol Oninaty Differ ilial Equations 

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The total pressure drop is evaluated by the general model (case 1), i.e. is the real one. The general model, case 1 (eqs. (5.572) and (5.575)) can be solved only by numerical methods, e.g. Polymath software. 

Living Example Problems POLYMATH software that allows students to explore ttie... 

In nonlinear least squares analysis we search for those parameter values that minimize the sum of squares of the differences between the measured values and the calculated values for all the data points. Many software programs are available to find these parameter values and all one has to do is to enter the data. The POLYMATH software will be used to illustrate this technique. In order to cany out the search efficiently, in some cases one has to enter initial estimates of the parameter values close to the actual values. These estimates can be obtained using the linear-least-squares technique just discussed. 

The companion CD-ROM provides additional learning resources such as sumniai notes, interactive computing modules, web modules, POLYMATH software to explore Tiviag example problems and ask what-if questions, and many more enrichment opportunities for both students and teachers. 

We will use the Polymath software package to express concentration as a funciic of time. Here we first choose the polynomial degree (in this ease, fourth degree) an then type in the values of at various limes t to obtain... 

Polymath. The Polymath software includes an ordinary differemial equation (ODE) solver, a nonlinear equation solver, and nonlinear regression. As with previous editions. Polymath is included with this ediiion to explore the example problems and to solve the home problems. A special Polymath web site iwtvn-.iMrlymaih-.spfrware.coin tniler) has been set up f(ar this book by Polymath authors Cutlip and Shacham. This weh site provides information on how to obtain an iqxluted version of Polymath at a discount. 

The solutions ai e only aiithmetic and Polymath software has been used. Note that T is in K and that the concentration of CO is in moPnri. Tlie conversion of ppm into mol/m is done by using the molai weight of CO (28 kg/kmol) and the density of air (1.09 kg/nri). 

One important paper by Shacham et al. (2002) presented a set of nonlinear systems from one- and multidimensional chemical engineering problems. The latter is available at www.polymath-software.com/hbrary. 

One-dimensional tests from the Web site www.polymath-software.com/library are implemented in C++ and adopted to validate the BzzFunctionRootRobust class. They are available in... 

POLYMATH (http //www.polymath-software.com) is a proven computational system, which has been specifically created for educational or professional use. The various POLYMATH programs allow the user to apply effective numerical analysis techniques during interactive problem-solving on personal computers. Results are presented graphically for easy understanding and for incorporation into papers and reports. Students, engineers, mathematicians, scientists, or anyone with a need to solve problems will appreciate the elSciency and speed of problem solution. 

Tliis problem focuses on using Polymath, an ordinary differential equation (ODE) solver, and also a non-linear equation (NLE) solver. Hiese equation solvers will be used extensively in later chapters. Infonnation on how to obtain and load the Polymath Software is given in Appendix E and on the DVD-ROM. (a) There are initially 400 rabbits (x) and 200 foxes (y) on Farmer Oat s property. Use Polymath or MATLAB to plot the concentration of foxes and rabbits as a function of time for a period of up to 600 days. The predator-prey relationships are given by the following set of coupled ordinary differential equations ... 

We are now in a position to express -r as a function of X and use the techniques in Chapter 2. However, we will use a better method to solw CRE problems, namely the Polymath software, discussed in the next chapter... 

Analysis Because there is no change in the net number of moles during this isothermal gas phase reaction occurring in a PBR, one can obtain an analytical solution to our CRE algorithm instead of using the Polymath software. Now let s look at what we could expect changing (he panicle diameter of the catalyst pellets. 

Information on how to obtain and load the Polymath software can be found in Appendix E. Tutorials can be found on the DVD-ROM home page under Living... 

Inrormation on how lo ohiain and load the Polymath software can be found in Appendix E. 

Polymath is an easy-to-use numerical computation package that allows students and professional.s to use personal computers to solve realistic, computationally intensive chemical reaction engineering problems. Polymath is unique in that the problems are entered just like their mathematical equations, and there is a minimal learning curve. The Polymath software package i.s uniquely suited for chemical reaction engineering as it is able lo. solve the following iype.s of problems that arise in CRE ... 

Note Getting Polymath. Many chemical engineering departments in the United Stales have a site license for Polymath and access to Polymath can be obtained from your departmental computing coordinator or instructor. In the event your department does not have a site license, have your professor contact or e-mail the CACHE Corporation at cache uts.cc.ulexas.edu. The latest information on Polymath is available from www.polymath-software.com. 

The Polymath authors have provided a free 15-day trial of Polymath on the DVD-ROM. After trying Polymath, your own version of the latest software can be purchased at a fantastically reduced price available only to users of this lexlbtwk by going to the special URL at www.polymath-software.com/fogler. Options for purchasing Polymath are only available at this special Web site where there are substantial discounts to the usual Polymath Educational version prices. To obtain this very special discounted price for Polymath, you may have to indicate where you are a student and the ISBN number of this text, which can be found on the copyright page. 

CACHE Corporation P.O. Box 7939 Austin. Texas 78713-7379 Web site www.polymath-software.com ogler/... 

The equations can be easily solved using the polymath program as shown in Figure 1.17 (for more details on Polymath software, see Appendix A). 

Assume velocity V, and calculate Reynolds number. From Reynolds number, calculate the friction factor from the Moody diagram shown in Figure 2.2, otherwise it can be obtained from the above-mentioned equations. Calculate the pressure drop and then compare the calculated result with the given value of pressure drop which is 118 kPa in the question of the example. Repeat until the desired pressure drop is reached. Polymath software can be used instead (Figure 2.19). The calculated velocity is 5.29 m/s as shown in Figure 2.20. 

Using polymath software (Table 5.1), results are shown in Figure 5.4. 

Using Polymath software (Figure A.l) you can solve systems consisting of the following forms ... 

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