Numerical Methods Using Matlab (4th Edition) Review

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Numerical Methods Using Matlab (4th Edition) ReviewWhether 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.
Numerical Methods Using Matlab (4th Edition) Overview 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.

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