Sinopsis
Mathematical modeling is the science or art of transforming any macro-scale or microscale problem to mathematical equations. Mathematical modeling of chemical and biological systems and processes is based on chemistry, biochemistry, microbiology, mass diffusion, heat transfer, chemical, biochemical and biomedical catalytic or biocatalytic reactions, as well as noncatalytic reactions, material and energy balances, etc. As soon as the chemical and biological processes are turned into equations, these equations must be solved efficiently in order to have practical value. Equations are usually solved numerically with the help of computers and suitable software.
Almost all problems faced by chemical and biological engineers are nonlinear. Most if not all of the models have no known closed form solutions. Thus the model equations generally require numerical techniques to solve them. One central task of chemical/ biological engineers is to identify the chemical/biological processes that take place within the boundaries of a system and to put them intelligently into the form of equations by utilizing justifiable assumptions and physico-chemical and biological laws. The best and most modern classification of different processes is through system theory. The models can be formed of steady-state design equations used in the design (mainly sizing and optimization), or unsteady-state (dynamic) equations used in start-up, shutdown, and the design of control systems. Dynamic equations are also useful to investigate the bifurcation and stability characteristics of the processes.
The complexity of the mathematical model depends upon the degree of accuracy required and on the complexity of the interaction between the different processes taking place within the boundaries of the system and on the interaction between the system and its surrounding. It is an important art for chemical/biological engineers to reach an optimal degree of sophistication (complexity) for the system model. By “optimal degree of sophistication” we mean finding a model for the process, which is as simple as possible without sacrificing the required accuracy as dictated by the specific practical application of the model. After the chemical/biological engineer has developed a suitable mathematical model with an optimal degree of “sophistication” for the process, he/she is then faced with the problem of solving its equations numerically. This is where stable and efficient numerical methods become essential. The classification of numerical solution techniques lends itself excellently to the system theory classification as well. A large number of chemical/biological processes will be presented, modeled, and efficient numerical techniques will be developed and programmed using MATLAB R 2. This is a sophisticated numerical software package. MATLAB is powerful numerically through its built-in functions and it allows us to easily develop and evaluate complicated numerical codes that fulfill very specialized tasks. Our solution techniques will be developed and discussed from both the chemical/biological point of view and the numerical point of view.
Content
- Computations and MATLAB
- Modeling, Simulation, and Design
- Some Models with Scalar Equations
- Initial Value Problems
- Boundary Value Problems
- Heterogeneous and Multistage Systems
- Industrial Problems
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