This book provides extensive problem-solving instruction and suggestions, numerous examples, and many complete and partial solutions in the main subject areas of chemical and biochemical engineering and related disciplines. Problem solutions are clearly developed using fundamental principles to create mathematical models. An equation-oriented approach that enables computer-based problem solving on personal computers is utilized. Efficient and effective problem solving is introduced employing numerical methods for linear equations, nonlinear equations, ordinary and partial differential equations, linear and nonlinear regressions, and polynomial curve fitting. Basic to advanced problem solving is covered utilizing a novel integrated approach with three widely used mathematical software packages: POLYMATH, Excel, and MATLAB. Readers may choose to focus on one or more of these software packages or utilize another mathematical software package.
The book and a dedicated web site (http://www.problemsolvingbook.com) furnish all necessary problem information, software files, and additional enrichment materials. For advanced applications, unique software tools are provided for solving complex problems such as parameter estimation in dynamic systems and solution of constrained systems of algebraic equations.
This book is intended for individuals who are interested in solving problems in chemical and biochemical engineering and in related fields by using mathematical software packages on personal computers. It can serve as a textbook for students in conjunction with college- and university-level courses, and it can be a companion reference book for individual students. For professionals, it can be an invaluable reference book that also allows extensive self-study in problem solving using the most widely used software packages.
Prior to the introduction of the personal computers and mathematical software packages in the early 1980's, desktop calculations for engineering problem solving were mainly carried out with hand-held calculators. Sometimes mainframe computers were utilized, which required source code programming. Since then the emphasis has gradually moved to computer-based (or computer-enhanced) problem solving or CBPS on desktop or notebook computers. By the time the first edition of this book was published in 1999, it became evident that CBPS can be a very important, or possibly the most important, application of the computer in scientific and engineering education and in industrial practice.
The first edition of this book provided examples to the use of CBPS in core chemical engineering subject areas using the POLYMATH software package. Shortly after the publication of the first edition, we carried out several comparison studies in order to determine what types of software packages should be included in the "toolbox" of the engineering student and the practicing engineer that would enable the effective and efficient solution of practical problems. We arrived at the conclusion that three types of software are needed. There is a need for a numerical problem solver, such as POLYMATH, that accepts the model equations close to their mathematical forms and provides their numerical solution with very minimal user intervention. Additionally, there is also a need to be able to use spreadsheet software, such as Excel, because of its wide use in business and industry. Software like Excel is also used for the organization and presentation of information in tabular and graphical forms and for database management-related operations. Software packages that support programming, such as MATLAB, are needed to implement algorithms which are required in graduate research and advanced mathematics, programming, control, and numerical analysis courses.
It is increasingly important for today's engineering student and forward-looking engineering professionals to be proficient in the use of several software packages, and thus we greatly expanded the book so that it now includes solutions in Excel and MATLAB, in addition to POLYMATH. New problems have been introduced that demonstrate how the special capabilities of each of these packages can best be utilized for efficient and effective problem solving.
The POLYMATH Numerical Computation Package
The POLYMATH package provides convenient solutions to most numerical analysis problems, including the problems that are presented in this book. We authored and published the first PC version of POLYMATH in 1984, and it has been in use since then in over one hundred universities and selected industrial sites world wide. The version available at the time of the publication of the book, POLYMATH 6.1, was released in 2006. This package contains the following programs:
Ordinary Differential Equations Solver
Nonlinear Algebraic Equations Solver
Linear Algebraic Equations Solver
Polynomial, Multiple Linear, and Nonlinear Regression Program
The programs are extremely easy to use, and all options are menu driven. Equations are entered in standard form with user-defined notation. Results are presented in graphical or tabular form. A sophisticated calculator and a general unit conversion utility are available within POLYMATH.
The new and unique capability of the latest POLYMATH to automatically export any problem to Excel and MATLAB with a single keypress is extensively utilized within this book. Automatic export to Excel includes all intrinsic functions and logical variables. A POLYMATH ODE_Solver Add-In is included for solving ordinary differential equations in Excel. Upon export to MATLAB, the equations are ordered in the computational sequence, the intrinsic functions and logical statements are converted, and a MATLAB function is generated. Template files to run the functions are available in the HELP section of POLYMATH or from the book's web site.
Current information on the latest POLYMATH software is available from http://www.polymath-software.com.
Many departments and some universities have obtained site licenses for POLYMATH. These licenses allow installation in all computer labs, and individual copies can be provided to all students, faculty and staff for use on personal computers. Detailed information is available from email@example.com
Use of This Book
This book is intended to serve as a companion text for the engineering student, the faculty instructor, or the practicing engineer. The instructions in the practical use of mathematical software package on representative problems from most chemical and biochemical engineering subject areas provide direct insight into problem setup and various practical aspects of numerical problem solving. For the undergraduate student at the early stages of his/her studies, the book can serve as the textbook for learning to categorize the problems according to the numerical methods that should be used for efficient and effective solutions. It provides basic instruction in the use of three popular and widely used software packages: POLYMATH, Excel, and MATLAB. Emphasis is on setting up problems and effectively obtaining the necessary solutions.
In addition to providing general numerical solving capabilities, the text gives problems in most subject areas so that it can serve as a reference book in most courses, as it provides example problems that can be illustrative of problems that may be assigned in the various courses. The book also provides help with problem solving in advanced level for problems often encountered in undergraduate and graduate research such as nonlinear regression, parameter estimation in differential systems, solving two-point boundary value problems and partial differential equations, constrained equation solving, and optimization.
For the practicing engineer, the book serves as resource book in computer-based problem solving. It provides a solid foundation in problem solving and can develop basic and advanced skills in the utilization of spreadsheets. Practical problems illustrate various problem solving approaches that can be implemented for problem formulation, problem solving, analysis, presentation of results, and documentation. Of particular interest is the coverage of the correlation and regression of data with statistical analysis. All of the book's problems can be solved with the Excel spreadsheet software that is widely used in industry.
Engineering faculty can use the book to introduce numerical methods into an individual course, a sequence of courses, or an entire departmental curriculum. This book provides supplementary problems that can be assigned to students in order to introduce numerical problem solving which is avoided in most textbooks. Many of the problems can be easily extended to open-ended problem solving so that critical thinking skills can be developed. The numerical solutions can be used to answer many "what if" type questions so that students can be encouraged to think about the implications of the problem solutions. The book can also be used as a companion textbook for an introductory computer programming course or a comprehensive course in numerical analysis.
All the chapters of the book, except the introductory Chapter 1, are built around problems that serve to provide practical applications in a particular subject area. Most of the problems presented in the book have the same general format for the convenience of the reader. The concise problem topic is followed by a listing of the engineering concepts demonstrated by the problem. Then the numerical methods utilized in the solution are indicated just before the detailed problem statement. Each of the problems presents the detailed equations and parameter values that are necessary for solution, including the appropriate units in a variety of systems, with Systeme International d'Unites (SI) being the most commonly used. Because of the wide variety of problems posed in this book, the notation used has been standardized according to one of the major Prentice Hall textbooks in the various subject areas whenever possible. Physical properties are either given directly in the problem or in the appendices.
The book is divided into two parts. In the first part, which includes the first six chapters, subjects of general interest are presented, some on an introductory level and some on an advanced level. In Chapter 1, Introduction, the history of CBPS is briefly reviewed and guidelines are provided for categorizing problems according to the numerical techniques that should be used for their solution. Chapter 2, Basic Principles and Calculations, serves a dual purpose. The chapter introduces the reader to the subject material that is typically taught in a first chemical engineering course (in most universities called Material and Energy Balance, or Stoichiometry). Additionally, this chapter demonstrates the use of POLYMATH for solving simple problems belonging to the main categories discussed in the book, namely single nonlinear algebraic equations, systems of linear algebraic equations, linear and polynomial regression, and systems of ordinary differential equations (ODEs).
In Chapter 3, Regression and Correlation of Data, the application of POLYMATH for analysis and regression of data using advanced statistical techniques is demonstrated. Chapter 4, Problem Solving with Excel, introduces the reader to the engineering and scientific problem solving capabilities of Excel using problems belonging to the same categories as in Chapter 2. The automatic export capabilities of POLYMATH to Excel are discussed. More advanced topics such as solution of systems of nonlinear algebraic equations (NLEs) and optimization with constraints (nonlinear programming) are also presented.
In Chapter 5, Problem Solving with MATLAB, MATLAB is used to solve the problems presented in Chapter 4. The capability of POLYMATH to automatically generate MATLAB m-files are presented and provided templates for MATLAB problem solutions are demonstrated and utilized. In Chapter 6, Advanced Techniques in Problem Solving, the problem solutions deal with advanced topics such as two-point boundary value problems, systems of differential-algebraic equations, partial differential equations, and parameter estimation in systems of differential equations.
The second part of the book (Chapters 7 through 14) is organized according to the particular subject areas such as Thermodynamics (Chapter 7), Fluid Mechanics (Chapter 8), and so forth. The content of these chapters is presented in the typical order of coverage in college or university-level courses.
New Content in the Second Edition
The contents of the book were almost doubled by adding six new chapters to the eight chapters of the first edition. The introductory Chapter 1 was added in order to help the reader in a very critical step of the problem solving--the characterization of the problem in terms of the solution method that has to be used.
After studying and verifying the importance of various software packages in effective and efficient problem solving, the two chapters dealing with the use of Excel and MATLAB were added. These chapters also introduce the new capability of the POLYMATH software to automatically convert a problem solution into Excel worksheets and MATLAB m-files. This considerably shortens the learning curve associated with the initial use of these packages.
Since the first edition was published, biochemical engineering has gained importance and is now being taught in most colleges and universities. The new biochemical engineering chapter and selected problems in other chapters provide a wide selection of problems in this important subject area. New chapters on "Phase Equilibria and Distillation" (Chapter 12) and "Process Dynamics and Control" (Chapter 13) have been added.
Companion Web Site
Readers of the book are encouraged to make full use of the companion web site that will be maintained and extended by the book's authors. This web site, http://www.problemsolvingbook.com/ , enables downloads of program files which are used in the various book chapters for the three software packages: POLYMATH, Excel, and MATLAB. Additional educational problems, learning resources, corrections and updates to this book, and new materials are provided.
The web site also allows book owners to purchase and immediately download the latest POLYMATH software at significant discounts from the already highly discounted POLYMATH Educational version software. This enables book users to have the very latest software at very reasonable cost.
Instructors who are using the book have special access to all problems as well as substantial educational and enrichment materials through the companion web site. This include suggestions as to the book use in individual courses, sequences of courses, and throughout a departmental curriculum. Details about this access are provided in Chapter 1 from the authors.
Chemical and Biochemical Engineering Departments
Academic departments are encouraged to consider adopting this book during the first introductory course in chemical and/or biochemical engineering and then utilizing the book as a supplement for many of the following courses in the curriculum. This allows an integrated approach to the use of numerical methods throughout the curriculum. This approach can be helpful in satisfying the ABET requirements for appropriate computer use in undergraduate studies.
A first course in numerical methods can also utilize many of the problems as relevant examples. In this application, the book will supplement a standard numerical methods textbook. Students will find the problems in this book to be more interesting than the strictly mathematical or simplified problems presented in many standard numerical analysis textbooks.