Symbolic solution

The result is that we get two sets of symbolic solutions forthe concentrations. The first set... 

There is no defined operation of division for matrices. However, a comparable result can be obtained by multiplying both sides of an equation (such as equation 4-2 by the inverse of matrix [A], The inverse (of matrix [A], for example) is conventionally written as [A]-1. Thus, the symbolic solution to equation 4-2 is generated by multiplying both sides of equation 4-2 by [A]-1 ... 

The systematic application of artificial intelhgence methods for the programmed manipulation of symbols in accordance with mathematical rules. Symbohc computing allows one to obtain symbolic solutions to equilibrium... 

Subramanian, V.R., White, R.E. Symbolic solutions for boundary value problems using Maple. Computers Chemical Engineering 24(11), 2405-2416 (2000)... 

The phases which occur are—Solid ice, sulphur dioxide hydrate, S02,7H20. Liquid two solutions, the one containing excess of sulphur dioxide, the other excess of water, and represented by the symbols (solution L), and H20t5 % tyS02 (solution II.). 

Mathematica can carry out both symbolic and numerical solutions of equations, including single algebraic equations, simultaneous algebraic equations, and differential equations, which we discuss later. Mathematica contains the rules needed for the symbolic solution of polynomial equations up to the fourth degree, and can... 

The statement DSolve is used to carry out a symbolic solution of a differential equation. We illustrate this with an example. 

Problem Write empirical formulas for the compounds named in Sample Problem 2.5. Plan We write the empirical formula by finding the smallest number of each ion that gives the neutral compound. These numbers appear as right subscripts to the element symbol. Solution... 

The result is that we get two sets of symbolic solutions for the concentrations. The first set appears to be the appropriate one as the leading coefficient is positive, whereas for the second set the same term is negative, suggesting that for real positive values of the parameters it would return negative concentrations, which are unphysical. Thus we can extract the first set of solutions with the bracketed number 1 ... 

Moreover, homework problems in engineering typically require either a numerical or a symbolic solution. For problems that require numerical solution, data is given. In contrast, in the symbolic soludon, the steps and the final answer are presented with variables that could be substituted with data, if necessary. The following example will demonstrate the difi rence between numerical and symbolic solutions. 

The general relationsfaip among pressure, and area is e qilained in detail in Chapter 10. At this time, don t worry about understanding these relationships. The purpose of this example is to demonstrate the difference between a numerical and a symbolic solution. The concepts that are used to solve this problem are Fi = == and F2 = iAJA Fi,... 

X Species Symbol / Solution vector for flow variables (X) Parameter for wall slip r Surface site density (mol/m )... 

Mathcad (http //www.mathcad.com) provides hundreds of operators and built-in functions for solving technical problems. Mathcad can be used to perform numeric calculations or to find symbolic solutions. It automatically tracks and converts units and operates on scalars, vectors, and matrices. 

Within the ME representation, one can make precise the symbolic solution to the e = 0 Schrodinger equation. 

Figure 11.1 Comparison of voltammetric data obtained at different potential sweep rates v for Cu(ll)-containing (solid lines) and Cu(ll)-free (symbols) solutions. The limiting currents of Cu(ll) reduction (dotted lines) served as base lines for the latter data.

Even in the presence of two elementary stages kinetic equations of successive reaction become noticeably more complicated, if at least one of them passes due to the patterns of second-order reaction. Mathematic analysis of such mechanisms with the object of symbolic solution of direct kinetic problem in Mathcad is difficult, therefore in this case it is appropriate to use Maple s analytic facilities. It is still possible to get integrated forms of equations for some kinetic schemes in Maple. 

C eval(Canal.Ch %Function evaluation for the symbolic solution... 

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