A Note about Numerical Solutions

Many of the problems considered in this course require the use of numerical methods for their solution. Many others can be solved manually, but it is probably easier to use numerical methods. For the most part, in this course there are six kinds of problems that will be solved numerically. These six problem types are (1) checking whether linear equations are mathematically independent, (2) solving sets of algebraic equations (and equations including exponentials and similar transcendental functions), (3) fitting linear models to experimental data, (4) fitting non-linear models to experimental data, (5) solving initial-value ordinary differential equations and (6) solving boundary value differential equations.

Each of these tasks can be accomplished using a number of software packages. It is not possible (or I am not willing) to describe how to use every possible software package to solve each type of problem. Still, no matter which software package one chooses to use, one generally must provide the same information and input data to that software. What differs is the specific way that the information and input is provided, and the details of how to run the software. Therefore, I have adopted the following approach in this course:

• There is a supplemental unit devoted to each problem type. Each supplemental unit begins by defining the problem type. It then lists the information and input data that are required for numerical solution of problems of that type, irrespective of the specific software being used. A brief description of what the numerical methods actually do to solve the problem follows. Finally, the use of MATLAB for solving that problem type is described. In most cases, either a MATLAB template file or a MATLAB script file is provided. This is done to minimize the amount of coding required of students, allowing them to focus on the kinetics and reaction engineering aspects of the problems. (Of course that only applies to those students who choose to use MATLAB.)
• Each time one of these problem types is encountered in an example or an in-class learning activity, the solution indicates the type of problem involved. It then states what information and input data will be required to solve the problem numerically, and proceeds to show how to generate the required input. After describing how to generate all required input, it presents the results one would obtain from a numerical solution, irrespective of the software used. If additional tasks remain after the numerical solution, their description follows immediately. In other words, the main bodies of the solutions generically describe how to set everything up for numerical solution, but they don't describe the specifics of doing so or of using any particular software.
• At the end of each example or in-class learning activity solution there is a final section that explains how to carry out the numerical solution using MATLAB and the template files and scripts available in the supplemental units. Students who choose to use software other than MATLAB can skip this section if they find that it doesn't help them to set up the solution using their software of choice. Faculty teaching the course and using software other than MATLAB might consider creating a handout or other documentation illustrating the use of that software.