Differentiability Excel spreadsheet

This appendix provides a detailed description of how to build Excel spreadsheet solutions for several of the problems that were presented and solved in Chapter 4. Generically, these include an ordinary-differential-equation boundary-value problem, a one-dimensional parabolic partial differential equation, and a two-dimensional elliptic partial differential equation. 

Statement, together with an Excel spreadsheet, to calculate the total amounts of substrate and biomass present at any of the indicated times, recognizing that at any time these totals are equal to the product of the volume of the cell-free growth medium and the corresponding concentration of biomass or glucose. The results of these calculations are summarized in Table 113.1-2, which also contains estimates of the total rates of consumption of substrate (-%) and production of biomass ( Kx) hat were obtained by simple numerical differentiation of the appropriate entries in Table 113.1-2 for example. 

Table A5.1 Excel Spreadsheet Designators and Formulas for Differential Permeation with Point Permeate Withdrawal Calculations...

The data is shown in the Excel spreadsheet below. We note that there are four initial concentrations of CO, and the conversion increases with increasing CO pressure. In order to use the differential method, we need to compare the rate of the reaction with the initial concentration of CO. The reaction rate is estimated from the data as... 

In this chapter we will encounter a number of standard mathematical operations that are conveniently performed and/or illustrated on a spreadsheet. We start with a brief description of the logic underlying the Goal Seek and Solver methods of Excel. Then we consider two methods often encountered in spectroscopy, viz. signal averaging and lock-in amplification. Subsequently the focus shifts toward numerical methods, such as peak fitting, integration, differentiation, and interpolation, some of which we have already encountered in one form or another in the context of least squares analysis and/or Fourier transformation. Finally we describe some matrix operations that are easy to perform with Excel. 

The challenge now is to solve this equation. An analytical, closed-form solution to Eqn. (7-12) does not exist. However, differential equations like this can be solved numerically using programs such as Matlab, Maple, or Mathcad. Appendix 7-A shows how to solve Eqn. (7-12) using a spreadsheet, i.e., EXCEL. From Appendix 7-A, the value of Cb at r = 40 min is 0.22 mol/1. 

All of this can be built into a mathematical model. It can be done with a spreadsheet like Microsoft Excel, breaking the detector thickness into 10 or 20 cells, or with more sophisticated computer programs, or solved in closed form using differential... 

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