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Numerical Methods Using MATLAB (3rd Edition), by John H. Mathews, Kurtis D. Fink
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This text provides an introduction to numerical analysis for either a single term course or a year long sequence. It is suitable for undergraduate students in mathematics, science, and engineering. Ample material is presented so that instructors will be able to select topics appropriate to their needs. *NEW-Replaces all pseudo-code algorithms with MATLAB programs, taking advantage of MATLABs widespread accessibility for educational instruction. *MATLABs structured programming style is easy for students to learn and resembles FORTRAN. *MATLAB allows for simple modification and in the exercises, students are encouraged to explore and compare modifications of algorithms. *Built-in MATLAB commands facilitate the plotting of numerical results from interpolation, curve fitting, differential equations, etc., thereby developing an important graphical understanding of problems and an invaluable sense of realism and enjoyment in numerical mathematics. *Provides a variety of examples and problems to develop and sharpen students skills in both the theory and practice of numerical analysis, includes easy-to-read proofs and worked-out examples. *Presents a wealth of tables and graphs to illustrate computer calculations in examples making the resulting numerical approximations easier to interpret. *Emphasizes why numerical methods work and their limitations, balances theory, error analysis, and readability, presents an error analysis for each method with an approach that is appropriate for the method at hand, but does not intimidate students, gives a mathematical derivation for each method that uses elementary results and builds students understanding of numerical analysis. *Offers computer assignments implementing the algorithms to give students an opportunity to practice their skills at scientific programming. *Details algorithms in pseudo-code. *Focuses on practical algorithms involving curve fitting, function approximations, numerical integration, linear systems solution, etc.
- Sales Rank: #694421 in Books
- Published on: 1998-12-23
- Original language: English
- Number of items: 1
- Dimensions: 9.75" h x 7.50" w x 1.50" l,
- Binding: Hardcover
- 662 pages
From the Back Cover
This introduction to numerical analysis shows how the mathematics of calculus and linear algebra are implemented in computer algorithms. It develops a deep understanding of why numerical methods work and exactly what their limitations are.
Most helpful customer reviews
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.
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.
1 of 1 people found the following review helpful.
A decent textbook without unnecessary clutter
By dhurandhar
This book goes straight to the heart of the numerical methods without unnecessary distracting fancy pictures and layout that some numerical methods textbook for engineers have. Also, the book has enough Matlab programs for a reader/student to understand essentials of Matlab programming and then tweak/modify the programs for further applications.
I wish author incorporates numerical methods for nonlinear ODE boundary value problems and eigenvalue problems related to ODE in the future edition.
Overall, it is an excellent introductory numerical methods textbook for science and engineering students. After grasping the fundamentals in this textbook, student/reader will tend to be more confident and enthusiastic while studying Numerical Analysis.
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