Linear Algebra with Applications

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 Part1 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. Key Features of the Eighth Edition: â [ Updated and revised throughout with new section material and exercises. â [ Each section begins with a motivating introduction, which ties material to the previously learned topics. â [ Carefully explained examples illustrate key concepts throughout the text. â [ Includes such new topics such as QR Factorization and Singular Value Decomposition. â [ Includes new applications such as a Leslie Matrix model that is used to predict birth and death patterns of animals. â [ 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. â [ 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. â [ Graphing Calculator Manual included as an appendix. â [ 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. â [ Available with WebAssign Online Homework & Assessment