An Introduction to Numerical Analysis for Electrical and Computer Engineers - Wiley
The subject of numerical analysis has a long history. In fact, it predates by cen-turies the existence of the modern computer. Of course, the advent of the modern
- Publisher: John Wiley & Sons (April 13, 2004)
- ISBN-10: 0471467375
- PDF 8,2 M
- 608 pages
computer in the middle of the twentieth century gave greatly added impetus to the
subject, and so it now plays a central role in a large part of engineering analysis,
simulation, and design. This is so true that no engineer can be deemed competent
without some knowledge and understanding of the subject. Because of the back-ground of the author, this book tends to emphasize issues of particular interest to
electrical and computer engineers, but the subject (and the present book) is certainly
relevant to engineers from all other branches of engineering.
Given the importance level of the subject, a great number of books have already
been written about it, and are now being written. These books span a c olossal
range of approaches, levels of technical difficulty, degree of specialization, breadth
versus depth, and so on. So, why should this book be added to the already huge,
and growing list of available books?
To begin, the present book is intended to be a part of the students’ first exposure
to numerical analysis. As such, it is intended for use mainly in the second year
of a typical 4-year undergraduate engineering program. However, the book may
find use in later years of such a program. Generally, the present book arises out of
the author’s objections to educational practice regarding numerical analysis. To be
more specific
1. Some books adopt a “ grocery list” or “recipes” approach (i.e., “methods” at
the expense of “analysis”) wherein several methods are presented, but with
little serious discussion of issues such as how they are obtained and their
relative advantages and disadvantages. In this genre often little consideration
is given to error analysis, convergence properties, or stability issues. When
these issues are considered, it is sometimes in a manner that is too superficial
for contemporary and future needs.
2. Some books fail to build on what the student is supposed to have learned
prior to taking a numerical analysis course. For example, it is common for
engineering students to take a first-year course in matrix/linear algebra. Ye t,
a number of books miss the opportunity to build on this material in a manner
that would provide a good bridge from first year to more sophisticated uses
of matrix/linear algebra in later years (e.g., such as would be found in digital
signal processing or state variable control systems courses).
3. Some books miss the opportunity to introduce students to the now quite vital
area of functional analysis ideas as applied to engineering problem solving.
Modern numerical analysis relies heavily on concepts such as function spaces,
orthogonality, norms, metrics, and inner products. Yet these concepts are
often considered in a very ad hoc way, if indeed they are considered at all.
4. Some books tie the subject matter of numerical analysis far too closely to
particular software tools and/or programming languages. But the highly tran-sient nature of software tools and programming languages often blinds the
user to the timeless nature of the underlying principles of analysis. Further-more, it is an erroneous belief that one can successfully employ numerical
methods solely through the use of “canned” software without any knowledge
or understanding of the technical details of the contents of the can. While
this does not imply the need to understand a s oftware tool or program down
to the last line of code, it does rule out the “black box” methodology.
5. Some books avoid detailed analysis and derivations in the misguided belief
that this will make the subject more accessible to the student. But this denies
the student the opportunity to learn an important mode of thinking that is a
huge aid to practical problem solving. Furthermore, by cutting the student
off from the language associated with analysis the student is prevented from
learning those skills needed to read modern engineering literature, and to
extract from this literature those things that are useful for solving the problem
at hand.
The prospective user of the present book will likely notice that it contains material
that, in the past, was associated mainly with more advanced courses. However, the
history of numerical computing since the early 1980s or so has made its inclusion
in an introductory course unavoidable. There is nothing remarkable about this. For
example, the material of typical undergraduate signals and systems courses was,
not so long ago, considered to be suitable only for graduate-level courses. Indeed,
most (if not all) of the contents of any undergraduate program consists of material
that was once considered far too advanced for undergraduates, provided one goes
back far enough in time.
