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This book provides a fundamental introduction to numerical analysis. This book covers numerous topics including Interpolation and Polynomial Approximation, Curve Fitting, Numerical Differentiation, Numerical Integration, and Numerical Optimization. For engineering and computer science fields.
- Sales Rank: #216186 in Books
- Published on: 2004-01-01
- Original language: English
- Number of items: 1
- Dimensions: 8.80" h x 1.60" w x 7.00" l, 2.74 pounds
- Binding: Paperback
- 696 pages
From the Back Cover
This book provides a fundamental introduction to numerical analysis. This book covers numerous topics including Interpolation and Polynomial Approximation, Curve Fitting, Numerical Differentiation, Numerical Integration, and Numerical Optimization. For engineering and computer science fields.
Excerpt. © Reprinted by permission. All rights reserved.
This book provides a fundamental introduction to numerical analysis suitable for undergraduate students in mathematics, computer science, physical sciences, and engineering. It is assumed that the reader is familiar with calculus and has taken a structured programming course. The text has enough material fitted modularly for either a single-term course or a year sequence. In short, the book contains enough material so that instructors will be able to select topics appropriate to their needs.
Students of various backgrounds should find numerical methods quite interesting and useful, and this is kept in mind throughout the book. Thus, there is a wide variety of examples and problems that help to sharpen one's skill in both the theory and practice of numerical analysis. Computer calculations are presented in the form of tables and graphs whenever possible so that the resulting numerical approximations are easier to visualize and interpret. MATLAB programs are the vehicle for presenting the underlying numerical algorithms.
Emphasis is placed on understanding why numerical methods work and their limitations. This is challenging and involves a balance between theory, error analysis, and readability. An error analysis for each method is presented in a fashion that is appropriate for the method at hand, yet does not turn off the reader. A mathematical derivation for each method is given that uses elementary results and builds the student's understanding of calculus. Computer assignments using MATLAB give students an opportunity to practice their skills at scientific programming.
Shorter numerical exercises can be carried out with a pocket calculator/computer, and the longer ones can be done using MATLAB subroutinie libraries. It is left for the instructor to guide the students regarding the pedagogical use of numerical computations. Each instructor can make assignments that are appropriate to the available computing resources. Experimentation with the MATLAB subroutine libraries is encouraged. These materials can be used to assist students in the completion of the numerical analysis component of computer laboratory exercises.
In this edition a section on Bezier curves has been added to the end of the chapter on curve fitting. Additionally, the chapter on numerical optimization has been expanded to include an introduction to both direct and derivative based methods for optimizing functions of one or more variables. A listing of the MATLAB programs in this textbook is available upon request from the authors (http://math.fullerton.edu/mathews/numerical.html). An instructor's solution manual for the exercise sets is available from the publisher. Previously, we took the attitude that any software program that students mastered would work fine. However, many students entering this course have yet to master a programming language (computer science students excepted). MATLAB has become the tool of nearly all engineers and applied mathematicians, and its newest versions have improved the programming aspects. So we think that students will have an easier and more productive time in this MATLAB version of our text.Most helpful customer reviews
12 of 22 people found the following review helpful.
Deceptive Title
By Lens Guy
This book was a waste of time for me. It's a decent numerical methods book but it's basically a textbook in Numerical Methods (which I already have).
Sprinkling a few lines of Matlab code in does not make it a Matlab book.
8 of 8 people found the following review helpful.
Satisfactory, but with flaws
By bliss
The Math Part:
I have to use this as the main text for a college math class, and while it may be a good reference book or engineering text, I don't think it's the best choice for a math course. It's written in such a way that you can flip to the section/topic you need and immediately get the main points and the formulas. But the authors don't necessarily teach their materials in the most intuitive way and frankly, don't seem that concerned with intuition at all. This makes the book quite sufficient as reference for your computations in your bioinformatics research project and such, but for a math text I would be more interested in really owning the intuition and tricky ideas so I can generalize to new cases or derive the formulas, rather than discovering 20 gazillion technical details/equations that will magically spew out an answer for who knows what reason. See the bajillion formulas on cubic splines for what I mean. Or see how instead of simple example + intuition, the authors chose to do 20 pages demonstrating Gaussian elimination.
The Matlab Part:
I learned Matlab in a few weeks from "Mastering MATLAB 7" and playing around with it on my own. It's very easy to just use the built-in manual or find all kinds of solutions to common problems using Google. There's really nothing wrong or tedious with picking up Matlab knowledge "from the manuals, man pages, the Internet, etc..." as one reviewer complained, because a language is necessarily something you pick up gradually and continually. Personally I think the reviewer was misleading in implying that this book does a good job teaching beginners Matlab. There's 1-2 programs per section, and no explanations in terms of the programming. Honestly, what are the chances that these programs will just drop into your lap and fit perfectly whatever application it is that you presumably need these numerical methods for? You will need to tailor the programs to your objectives or at least, understand WHY and HOW they work, in order to really take advantage of them, and that is outside the scope of this book. What this book really offers are the algorithms behind the programs, and not the programs themselves that are useful. In my opinion the Matlab programs were just a selling point, that's all.
There were also lots of little things that I personally just did not like about the book, where I felt the authors cut corners in their explanations or didn't phrase certain things in the best ways or used slightly funky notation or were not organized enough. Not a great math book in my opinion. But objectively speaking most people probably don't mind those kinds of details and aren't necessarily looking for a math book. So with that in mind I give it a 4.
16 of 18 people found the following review helpful.
Much needed book
By Amazon Customer
Whether you are an instructor for an Engineering class, Life Sciences, Statistics, Mathematics, or simply want to add practical mathematical analysis and programming, this book is the book you should use. I have been using Matlab for a number of years, and I had to pick up my Matlab knowledge from the manuals, man pages, the Internet, etc... and finding out the ins and outs of how to do something was not always an easy task nor accurate. Mathews and Fink's book put all you need to know about the most popular Mathematical methods at your finger tips. The book is tailored such that it can be used alone in a Mathematics course, or as reference in an Engineering course. One field of study that has enjoyed the power and flexibility of Matlab in the recent years is Computational Biology or Bioinformatics. Even though there are plenty of applications popping up here and there for this area of research, the area is still very much untapped and algorithms need to be developed for it as we go forward. Matlab is the best way to try out these new or improved algorithms, and use some of the available tools out there to generate C source code from your Matlab files. This method of algorithms development could save you tons of time, since Matlab makes numerical programming very simple.
The authors start with the basics in Numerical Methods; assuming that this book will be used as the primary text book in the course. A very good assumption, and the instructors who choose otherwise, can always skip the preliminaries. The context of text aims to provide a good balance of theory and application. One way that the authors try to keep this balance is to talk about "error" rate for the algorithms in question. The students are thought the limitations of Matlab along with the strengths of the software, and error analysis is one way to show the students that the results of numerical analysis is Matlab is not perfect, and more importantly why. This error analysis is done for every major algorithm and method presented in the text, and a number of methodologies are presented to help the student in figuring out this rate.
Authors start the main contents of the book with a representation of basic Linear Systems followed by a more complicated topic of Polynomial Approximation. Taylor Series and Lagrange Approximations are thoroughly covered in theory followed by examples that are solved by "hand" and by Matlab. The examples are complete, and can even be used, at least to start with, for the problem sets at the end of the chapter. As one would guess, curve fitting is the next topic of discussion. As you know, numerical techniques in science and engineering often requires curve fitting of experimental data. Starting with simple techniques of Least-Squares Lines, non-Linear Least-Square Methods and ending with the four different flavors of Spline Functions. The Matlab examples becomes more advanced as the topic progresses, and more and more examples are given as the topics get more complicated as well.
One can not learn Numerical Methods without a deep understanding of Numerical Differentiation and Numerical Integrations. Numerical methods for Differentiation are used to solve boundary value problems in ordinary differential equations and partial differential equations. Heat Transfer, Semiconductor Physics and Device Modeling, an Physical modeling of Molecules are just some of the examples that use these numerical differentiation techniques to solve problems. As is the case with the book, the authors start talking the theory behind how numerical differentiation works, and then, they go into the Matlab representation of the problem. Various approximation methods are presented, and error rate for each approximation method is also calculated in detail - both by hand and using Matlab.
Numerical Integration is a bit more difficult, as there are a number of ways to calculate the area under a curve. The authors present four numerical methods in detail: quadrature, composite trapezoidal, adaptive quadrature and Gauss-Legendre Integration. Each theory is followed by an example Matlab programs. The authors wrap up the text by talking about differential equations and partials differential equations. These two topics are difficult without using numerical methods, and it is even harder to follow the numerical theory of these topics. The authors take a slightly different approach to these topics. They start with examples from the get go. Instead of laying down the theory, they start each chapter with relevant examples from simple to more complex and abstract. Wave Equations and Heat Transfer equations are well known applications of PDE that are presented in detail. Eigenvalues, eigenvectors and the Jacodi's Meothod wrap up this text by j. H. Mathews and K. D. Fink.
I would recommend this book to be used for second year Mathematics, Physical Sciences or Engineering students. A course in Numerical Methods would benefit greatly from this book. Other students can certainly use this text to assist them with modeling, simulation and statistical problems in Electrical Engineering, Mechanical Engineering and various Applied Chemistry and Physics courses.
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