Updated and revised to increase clarity and further improve student learning, the Eighth Edition of Gareth Williams' classic text is designed for the introductory course in linear algebra. It provides a flexible blend of theory and engaging applications for students within engineering, science, mathematics, business management, and physics. It is organized into three parts that contain core and optional sections. There is then ample time for the instructor to select the material that gives the course the desired flavor.
Part 1 introduces the basics, presenting systems of linear equations, vectors and subspaces of Rn matrices, linear transformations, determinants, and eigenvectors.
Part 2 builds on the material presented in Part 1 and goes on to introduce the concepts of general vector spaces, discussing properties of bases, developing the rank/nullity theorem, and introducing spaces of matrices and functions.
Part 3 completes the course with important ideas and methods of numerical linear algebra, such as ill-conditioning, pivoting, and LU decomposition.
Throughout the text the author takes care to fully and clearly develop the mathematical concepts and provide modern applications to reinforce those concepts. The applications range from theoretical applications within differential equations and least square analysis, to practical applications in fields such as archeology, demography, electrical engineering and more. New exercises can be found throughout that tie back to the modern examples in the text.
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Features & Benefits
New and Key Features of the Eighth Edition:
Updated and revised throughout with new section material and exercises.
Each section begins with a motivating introduction, which ties material to the previously learned topics.
Carefully explained examples illustrate key concepts throughout the text.
Includes new topics such as QR Factorization and Singular Value Decomposition.
Includes new applications such as a Leslie Matrix model that is used to predict birth and death patterns of animals.
Includes discussions of the role of linear algebra in many areas, such as the operation of the search engine Google and the global structure of the worldwide air transportation network.
A MATLAB manual that ties into the regular course material is included as an appendix. These ideas can be implemented on any matrix algebra software package. This manual consists of 28 sections that tie into the regular course material.
Graphing Calculator Manual included as an appendix.
A Student Solutions Manual that contains solutions to selected exercises is available as a supplement. An Instructors Complete Solutions Manual, test bank, and PowerPoint Lecture Outlines are also available.
Available with WebAssign Online Homework & Assessment
The ideal text for the undergraduate Linear Algebra course.
Part 1 Linear Equations, Vectors, and Matrices
Chapter 1 Linear Equations and Vectors
Chapter 2 Matrices and Linear Transformations
Chapter 3 Determinants and Eigenvectors
Part 2 Vector Spaces
Chapter 4 General Vector Spaces
Chapter 5 Coordinate Representations
Chapter 6 Inner Product Spaces
Part 3 Numerical Linear Algebra
Chapter 7 Numerical Methods
Chapter 8 Linear Programming
Gareth Williams-Stetson University
Gareth Williams earned a B.S. and a Ph.D. in applied mathematics from the University of Wales, and did graduate work at Kings College University of London. He has taught mathematics at the University of Florida, the University of Denver, and Stetson University. He has been an exchange professor at the Paedagogische Hochschule, in Freiburg, Germany and has spent sabbaticals at the University of Wales. His mathematical interests include linear algebra, relativity, mathematical modeling, and the computer in mathematics education.
His publications include "Fine Topologies for Minkowski Space", Motions in Relativistic Space", "Mathematics in Archaeology", and books on Finite Mathematics, Calculus, and College Algebra. He is the co-developer (with Lisa Coulter) of the linear algebra software package, "The Linear Algebra Toolbox" for MATLAB. Dr. Williams is a member of The Mathematics Association of America.
Additional Titles by this Author
- ISBN-13: 9781449679569
- ISBN-13: 9781449687892
- ISBN-13: 9781449687922