Numerical Methods for Chemical Engineering: Applications in MATLAB 1st Edition by Kenneth J. Beers.
Contents:
1 Linear algebra
2 Nonlinear algebraic systems
3 Matrix eigenvalue analysis
4 Initial value problems
5 Numerical optimization
6 Boundary value problems
7 Probability theory and stochastic simulation
8 Bayesian statistics and parameter estimation
9 Fourier analysis
Preface by Kenneth J. Beers:
This text focuses on the application of quantitative analysis to the field of chemical engineering. Modern engineering practice is becoming increasingly more quantitative, as the use of scientific computing becomes ever more closely integrated into the daily activities of all engineers. It is no longer the domain of a small community of specialist practitioners. Whereas in the past, one had to hand-craft a program to solve a particular problem, carefully husbanding the limited memory and CPU cycles available, now we can very quickly solve far more complex problems using powerful, widely-available software. This has introduced the need for research engineers and scientists to become computationally literate – to know the possibilities that exist for applying computation to their problems, to understand the basic ideas behind the most important algorithms so as to make wise choices when selecting and tuning them, and to have the foundational knowledge necessary to navigate independently through the literature.
This text meets this need, and is written at the level of a first-year graduate student in chemical engineering, a consequence of its development for use at MIT for the course 10.34, “Numerical methods applied to chemical engineering.” This course was added in 2001 to the graduate core curriculum to provide all first-year Masters and Ph.D. students with an overview of quantitative methods to augment the existing core courses in transport phenomena, thermodynamics, and chemical reaction engineering. Care has been taken to develop any necessary material specific to chemical engineering, so this text will prove useful to other engineering and scientific fields as well. The reader is assumed to have taken the traditional undergraduate classes in calculus and differential equations, and to have some experience in computer programming, although not necessarily in A AB ®. Even a cursory search of the holdings of most university libraries shows there to be a great number of texts with titles that are variations of “Advanced Engineering Mathematics” or “Numerical Methods.” So why add yet another?
I find that there are two broad classes of texts in this area. The first focuses on introducing numerical methods, applied to science and engineering, at the level of a junior or senior undergraduate elective course. The scope is necessarily limited to rather simple techniques and applications. The second class is targeted to research-level workers, either higher graduate-level applied mathematicians or computationally-focused researchers in science and engineering. These may be either advanced treatments of numerical methods for mathematicians, or detailed discussions of scientific computing as applied to a specific subject such as fluid mechanics.
Neither of these classes of text is appropriate for teaching the fundamentals of scientific computing to beginning chemical engineering graduate students. Examples should be typical of those encountered in graduate-level chemical engineering research, and while the students should gain an understanding of the basis of each method and an appreciation of its limitations, they do not need exhaustive theory-proof treatments of convergence, error analysis, etc. It is a challenge for beginning students to identify how their own problems may be mapped into ones amenable to quantitative analysis; therefore, any appropriate text should have an extensive library of worked examples, with code available to serve later as templates. Finally, the text should address the important topics of model development and parameter estimation. This book has been developed with these needs in mind.
This text first presents a fundamental discussion of linear algebra, to provide the necessary foundation to read the applied mathematical literature and progress further on one’s own. Next, a broad array of simulation techniques is presented to solve problems involving systems of nonlinear algebraic equations, initial value problems of ordinary differential and differential-algebraic (DAE) systems, optimizations, and boundary value problems of ordinary and partial differential equations. A treatment of matrix eigenvalue analysis is included, as it is fundamental to analyzing these simulation techniques.
Next follows a detailed discussion of probability theory, stochastic simulation, statistics, and parameter estimation. As engineering becomes more focused upon the molecular level, stochastic simulation techniques gain in importance. Particular attention is paid to Brownian dynamics, stochastic calculus, and Monte Carlo simulation. Statistics and parameter estimation are addressed from a Bayesian viewpoint, in which Monte Carlo simulation proves a powerful and general tool for making inferences and testing hypotheses from experimental data.
In each of these areas, topically relevant examples are given, along with A AB www atw r s c programs that serve the students as templates when later writing their own code. An accompanying website includes a A AB tutorial, code listings of all examples, and a supplemental material section containing further detailed proofs and optional topics. Of course, while significant effort has gone into testing and validating these programs, no guarantee is provided and the reader should use them with caution.
The problems are graded by difficulty and length in each chapter. Those of grade A are simple and can be done easily by hand or with minimal programming. Those of grade B require more programming but are still rather straightforward extensions or implementations of the ideas discussed in the text. Those of grade C either involve significant thinking beyond the content presented in the text or programming effort at a level beyond that typical of the examples and grade B problems. The subjects covered are broad in scope, leading to the considerable (though hopefully not excessive) length of this text.
The focus is upon providing a fundamental understanding of the underlying numerical algorithms without necessarily exhaustively treating all of their details, variations, and complexities of use. Mastery of the material in this text should enable first-year graduate students to perform original work in applying scientific computation to their research, and to read the literature to progress independently to the use of more sophisticated techniques.
The problems are graded by difficulty and length in each chapter. Those of grade A are simple and can be done easily by hand or with minimal programming. Those of grade B require more programming but are still rather straightforward extensions or implementations of the ideas discussed in the text. Those of grade C either involve significant thinking beyond the content presented in the text or programming effort at a level beyond that typical of the examples and grade B problems.
The subjects covered are broad in scope, leading to the considerable (though hopefully not excessive) length of this text. The focus is upon providing a fundamental understanding of the underlying numerical algorithms without necessarily exhaustively treating all of their details, variations, and complexities of use. Mastery of the material in this text should enable first-year graduate students to perform original work in applying scientific computation to their research, and to read the literature to progress independently to the use of more sophisticated techniques.
Book Details:
⏩Edition: 1st Edition
⏩Author: Kenneth J. Beers
⏩Puplisher: Cambridge University Press
⏩Puplication Date: October 30, 2006
⏩Language: English
⏩Pages: 488
⏩Size: 5.40 MB
⏩Format: PDF
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