Introduction to Numerical Methods and MATLAB: Implementations and Applications (Hardcover)

This book is a thoroughly modern exposition of classic numerical methods using MATLAB. The fundamental theory of each method is briefly developed. Rather than providing a detailed numerical analysis, the behavior of the methods is exposed by carefully designed numerical experiments. The methods are then exercised on several nontrivial example problems from engineering practice. The material in each chapter is organized as a progression from the simple to the complex. This leads the student to an understanding of the sophisticated numerical methods that are part of MATLAB. An integral part of the book is the Numerical Methods with MATLAB (NMM) Toolbox, which provides 150 programs and over forty data sets. The NMM Toolbox is a library of numerical techniques implemented in structured and clearly written code.

This book is an introduction to MATLAB and an introduction to numerical methods. It is written for students of engineering, applied mathematics, and science. The primary objective of numerical methods is to obtain approximate solutions to problems that are not obtainable by other means. This book teaches how the core techniques of numerical methods are used to solve otherwise unsolvable problems of modern technological significance.

The outstanding pedagogical features of this book are:

• use of numerical experiments as a means of learning why numerical methods work and how they fail
• a separate chapter reviewing the basics of applied linear algebra, and how computations involving matrices and vectors are naturally expressed in MATLAB
• use of a range of examples from those that provide a succinct illustration of a basic algorithm, to those that develop solutions to substantial problems in engineering
• consistent use of well-documented and structured code written in the MATLAB idiom
• a library of general purpose routines—the NMM Toolbox—that are readily applied to new problems
• a progressive approach to algorithm development leading the reader to an understanding of the more sophisticated routines in the built-in MATLAB toolbox.

The primary goals of the book are to provide a solid foundation in applied computing, and to demonstrate the implementation and application of standard numerical methods to practical problems. This is achieved by a systematic development of techniques beginning with the simple and ending with the sophisticated. Good programming practice is used throughout to show the reader how to clearly express and document computational ideas. By providing an extensive library of working codes, as well as an exposition of the methods used by the built-in MATLAB toolbox, the reader is challenged by the application of numerical methods to practical problems. This bypasses the ritual of forcing the reader to reinvent simple programs that fail on more technologically significant, practical problems.

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