As an engineering student or professional, you are almost always involved in numerical problem solving on a personal computer. The objective of this book is to enable you to solve numerical problems that you may encounter in your student or professional career in a most effective and efficient manner. The tools that are typically used for engineering or technical problem solving are mathematical software packages that execute on personal computers on the desktop. In order to solve your problems most efficiently and accurately, you must be able to select the appropriate software package for the particular problem at hand. Then you must also be proficient in using your selected software tool.
In order to help you achieve these objectives, this book provides a wide variety of problems from different areas of chemical, biochemical, and related engineering and scientific disciplines. For some of these problems, the complete solution process is demonstrated. For some problems, partial solutions or hints for the solution are provided. Other problems are left as exercises for you to solve.
Most of the chapters of the book are organized by chemical and biochemical engineering subject areas. The various chapters contain between five and twenty-eight problems that represent many of the problem types that require a computer solution in a particular subject area. All problems presented in the book have the same general format for your convenience. The concise problem topic is first followed by a listing of the engineering or scientific concepts demonstrated by the problem. Then the numerical methods utilized in the solution are indicated just before the detailed problem statement is presented. Typically a particular problem presents all of the detailed equations that are necessary for solution, including the appropriate units in a variety of systems, with Système International d’Unités (SI) being the most commonly used. Physical properties are either given directly in the problem or in the appendices. Complete and partial solutions are provided to many of the problems. These solutions will help you learn to formulate and then to solve the unsolved problems in the book as well as the problems that you will face in your student and/or professional career.
Three widely used mathematical software packages are used in this book for solving the various problems: POLYMATH,[*] Excel,[†] and MATLAB.[‡] Each of these packages has specific advantages that make it the most appropriate for solving a particular problem. In some cases, a combined use of several packages is most desirable. These mathematical software packages that solve the problems utilize what are called “numerical methods.” This book presents the fundamental and practical approaches to setting up problems that can then be solved by mathematical software that utilizes numerical methods. It also gives much practical information for problem solving. The details of the numerical methods are beyond the scope of this book, and reference can be made to textbook by Constantinides and Mostoufi.[1] More advanced and extensive treatment of numerical methods can be found in the book of Press et al.[2]
The first step in solving a problem using mathematical software is to prepare a mathematical model of the problem. It is assumed that you have already learned (or you will learn) how to prepare the model of a problem from in particular subject area (such as thermodynamics, fluid mechanics, or biochemical engineering). A general approach advocated in this book is to start with a very simple model and then to make the model more complex as necessary to describe the problem. Engineering and scientific fundamentals are important in model building. The first step in the solution process is to characterize the problem according to the type of the mathematical model that is formulated: a system of algebraic equations or a system of ordinary differential equations, for example. When the problem is characterized in these terms, the software package that efficiently solves this type of problems can be utilized. Most of the later part of this chapter is devoted to learning how to characterize a problem in such mathematical terms.
In order to put the use of mathematical software packages for problem solving into proper perspective, it is important and interesting to review the history in which manual problem solving has been replaced by numerical problem solving.
Leave a Reply