Symbolic-Numeric Computations for Problem-Solving in Physical Chemistry and Biochemistry

The combination of symbolic and numeric computation techniques leads to new approaches for problem-solving in areas of applied mathematics and science. It is shown, in examples from Physical Chemistry and Biochemistry, how the use of a modern computer algebra system such as Maple enables an automatic and computerized solution of problems in ways that are not possible with conventional computing systems. In our first example we study the thermodynamic behavior of steam reforming reactions and determine the temperature and pressure dependence of the chemical compositions at equilibrium. Using Maple's symbolic computation capabilities a system of nonlinear equations for the reaction extents is derived. For the fast numerical solution of the nonlinear equations the Newton-Raphson algorithm is applied. A FORTRAN preprocessor in Maple calculates the Jacobian matrix needed for this algorithm and generates a complete and ready-to-compile FORTRAN program. In the second example we demonstrate how the McConnell equations in Biochemistry, a linear inhomogeneous system of differential equations with constant coefficients, can be solved analytically in a direct way by using Maple's symbolic linear algebra routines. In addition, the automatic generation of numerical code for the determination of the formal parameters involved in the solutions is described