Integration POLYMATH software

Softwares for numerical integration of equations include the calculator HP-32SII, POLYMATH, CONSTANTINIDES AND CHAPRA CANALE. The last of these also can handle tabular data with variable spacing. POLYMATH fits a polynomial to the tabular data and then integrates. A comparison is made in problem PI.03.03 of the integration of an equation by the trapezoidal and Runge-Kutta rules. One hundred intervals with the trapezoidal rule takes little time and the result is usually accurate enough, so it is often convenient to standardize on this number. 

Absorbance was measured at 25 nm intervals from 325 nm to 500 nm. These values were converted to absorptivity (L g-1 cm-1) and the area under the curve was integrated from 350 nm to 500 nm using software by PolyMath Control Data ( 1984). This value was compared to corresponding values obtained with the starting material (lignin or HPL), and the color loss was calculated from... 

With these additional relationships, one observes that if the rate law is given and the concentrations can be expressed as a function of conversion, ilwn in fact tee have — as a ftmcrhn of X and this is all ihal is needed to ewiuaie ihe design ecjuatimis. One can u.se either the numerical techniques described in Chapter 2. or, as we shall see in Chapter 4, a table of integrals, and/or software programs (e.g.. Polymath). 

The differential and integral methods are used primarily in analyzing batch reactor data. Because a number of software packages (e.g.. Polymath, MATLAB) are now available to analyze data, a rather extensive discussion of nonlinear regression is included. 

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