Page 10 - Numerical Methods for Chemical Engineering

x Preface

Neither of these classes of text is appropriate for teaching the fundamentals of scientific
computing to beginning chemical engineering graduate students. Examples should be typ-
ical 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.
Thistextfirstpresentsafundamentaldiscussionoflinearalgebra,toprovidethenecessary
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 esti-
mation 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 AAB
www atw r s c programs that serve the students as templates when later writing
their own code. An accompanying website includes a AAB 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
requiremoreprogrammingbutarestillratherstraightforwardextensionsorimplementations
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.