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Matrix Operations for Engineers and Scientists

An Essential Guide in Linear Algebra

  • Textbook
  • © 2010

Overview

Authors:
  1. Alan Jeffrey

    1. University of Newcastle, Newcastle upon Tyne, United Kingdom

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  • Carefully explains each operation with matrices and offers many worked examples to show how to use these operations
  • Provides exercises with each chapter - solutions at the end of the book
  • Explains how matrices can be used for solving homogeneous and non-homogeneous differential equations
  • Introduces linear algebra in a context that engineers and science students can understand
  • Supplies the foundation required to intelligently use and interpret results of computer-algebra packages
  • Includes supplementary material: sn.pub/extras

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-xi
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  2. Matrices and Linear Systems of Equations

    • Alan Jeffrey
    Pages 1-11

  3. Determinants, and Linear Independence

    • Alan Jeffrey
    Pages 13-34

  4. Matrix Multiplication, the Inverse Matrix and Partitioning

    • Alan Jeffrey
    Pages 35-74

  5. Systems of Linear Algebraic Equations

    • Alan Jeffrey
    Pages 75-99

  6. Eigenvalues, Eigenvectors, Diagonalization, Similarity, Jordan Normal Forms, and Estimating Regions Containing Eigenvalues

    • Alan Jeffrey
    Pages 101-158

  7. Systems of Linear Differential Equations

    • Alan Jeffrey
    Pages 159-205

  8. An Introduction to Vector Spaces

    • Alan Jeffrey
    Pages 207-237

  9. Linear Transformations and the Geometry of the Plane

    • Alan Jeffrey
    Pages 239-272

  10. Back Matter

    Pages 273-314
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Keywords

About this book

Engineers and scientists need to have an introduction to the basics of linear algebra in a context they understand. Computer algebra systems make the manipulation of matrices and the determination of their properties a simple matter, and in practical applications such software is often essential. However, using this tool when learning about matrices, without first gaining a proper understanding of the underlying theory, limits the ability to use matrices and to apply them to new problems. This book explains matrices in the detail required by engineering or science students, and it discusses linear systems of ordinary differential equations. These students require a straightforward introduction to linear algebra illustrated by applications to which they can relate. It caters of the needs of undergraduate engineers in all disciplines, and provides considerable detail where it is likely to be helpful. According to the author the best way to understand the theory of matrices is by working simple exercises designed to emphasize the theory, that at the same time avoid distractions caused by unnecessary numerical calculations. Hence, examples and exercises in this book have been constructed in such a way that wherever calculations are necessary they are straightforward. For example, when a characteristic equation occurs, its roots (the eigenvalues of a matrix) can be found by inspection. The author of this book is Alan Jeffrey, Emeritus Professor of mathematics at the University of Newcastle upon Tyne. He has given courses on engineering mathematics at UK and US Universities.

Reviews

From the reviews:

“This work addresses all of the standard fare associated with an introductory course in linear algebra, albeit with an applied perspective appropriate for the audience suggested by its title. … Readers wishing to apply the methods of linear algebra to engineering problems would certainly find this book appropriate. … Summing Up: Recommended. Academic libraries serving upper-division undergraduates through researchers/faculty.” (D. S. Larson, Choice, Vol. 48 (7), March, 2011)

“This book meets the needs of engineers and scientists for an introduction to linear algebra in a context they understand. It provides a very detailed treatment of the theory of matrices … . There are numerous worked examples throughout the book and sets of exercises are provided at the end of each chapter, with all the solutions given at the end of the book. A special effort is made to keep all numerical calculations simple.” (Rabe von Randow, Zentralblatt MATH, Vol. 1210, 2011)

Authors and Affiliations

  • University of Newcastle, Newcastle upon Tyne, United Kingdom

    Alan Jeffrey

About the author

Alan Jeffrey is emeritus professor of engineering mathematics at Newcastle. He has had a distinguished career which included work at University of Delaware, Stanford, Wisconsin and City University Hong Kong. He has published 14 books, some at undergraduate level and others at the research monograph level, some with Springer, and his sales records look very good. He also is well known because he edited some important reference works such as the Handbook of Mathematical Formula.

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