Computer programs Matlab

The holistic thermodynamic approach based on material (charge, concentration and electron) balances is a firm and valuable tool for a choice of the best a priori conditions of chemical analyses performed in electrolytic systems. Such an approach has been already presented in a series of papers issued in recent years, see [1-4] and references cited therein. In this communication, the approach will be exemplified with electrolytic systems, with special emphasis put on the complex systems where all particular types (acid-base, redox, complexation and precipitation) of chemical equilibria occur in parallel and/or sequentially. All attainable physicochemical knowledge can be involved in calculations and none simplifying assumptions are needed. All analytical prescriptions can be followed. The approach enables all possible (from thermodynamic viewpoint) reactions to be included and all effects resulting from activation barrier(s) and incomplete set of equilibrium data presumed can be tested. The problems involved are presented on some examples of analytical systems considered lately, concerning potentiometric titrations in complex titrand + titrant systems. All calculations were done with use of iterative computer programs MATLAB and DELPHI. 

Equation (27) expresses an error in the dynamic matrix element Lij obtained from full matrix analysis if the error in peak volumes is Aa [50]. It also assumes that volume errors are equal for all peaks and are uncorrelated Aa is volume error normalized to the volume of a single spin at Tm = 0. Modem computer programs (Matlab, Mathematica, Mapple) can calculate the dynamic matrix from eq. (11) directly. 

The computer program MATLAB was used to solve the differential equations for the concentrations versus batch time, according to Figure 20.20. 

It was indicated that the original method can be extended on systems where two or three analytes can be determined from a single titration curve. The shifts DpH affected by j-th PT addition should be sufficiently high it depends on pH value, a kind and concentration of the buffer chosen and its properties. The criterion of choice of the related conditions of analysis has been proposed. A computer program (written in MATLAB and DELPHI languages), that enables the pH-static titration to be done automatically, has also been prepared. 

Data collection and evaluation were carried out by supplied Jasco software. A custom-built computer program developed using MatLab (Mathworks Corp.) was used for quantitative analysis of CD spectra to calculate the relative composition of the spectra. 

This Appendix contains four computer programs in MatLab that can be used by the reader to perform typical calculations related to shelf-life estimations. 

With these five equations (Eqs. 23-42 to 23-46), two of them partial differential equations, the limits of the analytical approach and the goals of this book are clearly exceeded. However, at this point we take the occasion to look at how such equations are solved numerically. User-friendly computer programs, such as MAS AS (Modeling of Anthropogenic Substances in Aquatic Systems, Ulrich et al., 1995) or AQUASIM (Reichert, 1994), or just a general mathematical tool like MATLAB and MATHE-MATICA, can be used to solve these equations for arbitrary constant or variable parameters and boundary conditions. 

The computer program for solving the nonlinear programming problem (9) was developed using Matlab, applying the simplex method for searching the optimal solution. 

We illustrate the theoretical concepts in a few selected computer programs and then apply them to realistic examples. MATLAB [5] is the programming language of choice for most chemometricians. The MATLAB code provided in the examples is intended to encourage and guide readers to write their own programs for their... 

A number of standard computer programs easily handle problems of this type such as spreadsheet packages, Matlab, Mathcad, Polymath, and so on as well as symbolic manipulators such as Mathematica, Maple, Derive, etc. Most statistic packages and equation solvers will also solve linear equations and have a simple user interface. 

The following problems require use of a spreadsheet program such as Microsoft Excel or a computational programming enviromnent such as Matlab . 

Use a circuit with Re = 10 Qcm, Rf = 100 Ocm, and Qi = 20 iF/cm to verify the equations given in Table 22.1. This problem requires use of a spreadsheet program such as Microsoft Excel or a computational programming environment such as Matlab . 

This book demonstrates four computer programs Excel , MATLAB , Aspen Plus , and FEMLAB . You may have access to other programs created by other companies. While the exact details will not be the same, the steps you take will be similar. 

To solve equations of state, you must solve algebraic equations as described in this chapter. Later chapters cover other topics governed by algebraic equations, such as phase equilibrium, chemical reaction equilibrium, and processes with recycle streams. This chapter introduces the ideal gas equation of state, then describes how computer programs such as Excel , MATLAB , and Aspen Plus use modified equations of state to easily and accurately solve problems involving gaseous mixtures. 

In MATLAB you write computer programs that are called m-files and are saved on your computer. The files can be used at any time by simply typing their name in the command line, and one m-file can use another m-file. You will want to include comments in your m-file that explain what the file does. This is done by inserting a % everything after % on a line is considered a comment. These comments remind you of details when you come back to the program at a later time. 

The equations to be solved are first the Peng-Robinson equation of Eqs. 6.7-1 to 6.7-4 for the initial molar volume or compressibility, and then the initial number of moles in the tank using Eq. d of Illustration 6.5-2. The results, using the Visual Basic computer program described in Appendix B.I-2, the DOS-based program PRl described in Appendix B.II-1, the MATHCAD worksheet described in Appendix B.ni, or the MATLAB program described in B.IV included... 

Write two computer programs, one in FORTRAN and one in MATLAB, that calculate the feedback controller gain Kc that gives a maximum closedloop log modulus of + 2 dB for a process with the openloop transfer function... 

If you don t like solving by hand, there are numerous computer programs out there to help you solve equations like this, such as MATLAB, POLYMATH, and many others. You ll probably want to learn how to use the one your school prefers eventually so why not now ... 

To summarize, we perform a singular value decomposition of the augmented formula matrix to obtain the matrices U, W, and V. With these, we use (11.2.10) to obtain a particular basis vector N for the range. From V, we form P and then use (11.2.7) to obtain all sets of stoichiometric coefficients Vy. Then we combine N and Vy into (11.2.5) to determine all sets of mole numbers that satisfy the elemental balances. Therefore, a singular value decomposition provides the number of independent reactions 91, all sets of 91 independent stoichiometric coefficients Vy, and all possible combinations of mole numbers N that satisfy the elemental balances. A computer program for performing the decomposition is contained in the book by Press et al. [9] routines for performing the decomposition are also available in MATLAB and in Mathematica . 

When writing a computer program, often it becomes necessary to execute a line or a block of yoiu-computer code many times. MATLAB provides and u>AiU commands for such situations. 

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