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Linear Algebra with ApplicationsAuthor: Gareth Williams
Linear Algebra with Applications, Ninth Edition is designed for the introductory course in linear algebra for students within engineering, mathematics, business management, and physics. Updated to increase clarity and improve student learning, the author provides a flexible blend of theory and engaging applications.
The material in Linear Algebra with Applications, Ninth Edition is arranged into three parts that contain core and optional sections:
Part 1 introduces the basics, discussing systems of linear equations, vectors in Rn matrices, linear transformations, determinants, eigenvalues, and eigenspaces.
Part 2 builds on this material to discuss general vector spaces, and includes such topics as the Rank/Nullity Theorem, inner products and coordinate representation.
Part 3 completes the course with important ideas and methods in Numerical Linear Algebra including ill-conditioning, pivoting, LU decomposition and Singular Value Decomposition.
Throughout the text the author provides interesting applications, ranging from theoretical applications such as the use of linear algebra in differential equations, to many practical applications in the fields of electrical engineering, traffic analysis, relativity, history, and more.
TABLE OF CONTENTS
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
Appendix A Cross Product
Appendix B Equations of Planes and Lines in Three-Space
Appendix C Graphing Calculator Manual
Appendix D MATLAB Manual