Matrix Operations for Engineers and Scientists: An Essential Guide in Linear Algebra

Book Preface

This book is based on many courses given by the author to English and American undergraduate students in engineering and the applied sciences. The book separates naturally into two distinct parts, although these are not shown as parts one and two. The first part, represented by Chapters 1–4 and a large part of Chapter 5, gives a straightforward account of topics from the theory of matrices that form part of every basic mathematics course given to undergraduate students in engineering and the applied sciences. However, the presentation of the basic material given in this book is in greater detail than is usually found in such courses. The only unusual topics appearing in the first part of the book are in Chapter 3. These are the inclusion of the technique of least-squares fitting of polynomials to experimental data, and the way matrices enter into a finite difference approximation for the numerical solution of the Laplace equation. The least-squares fitting of polynomials has been included because it is useful and provides a simple application of matrices, while the finite difference approximation for the Laplace equation shows how matrices play a vital part in the numerical solution of this important partial differential equation. This last application also demonstrates one of the ways in which very large matrix equations can be generated when seeking the numerical solution of certain types of problem.