Linear Algebra: A Modern Introduction (with CD-ROM) / Edition 2

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Overview

David Poole's innovative book emphasizes vectors and geometric intuition from the start and better prepares students to make the transition from the computational aspects of the course to the theoretical. Poole covers vectors and vector geometry first to enable students to visualize the mathematics while they are doing matrix operations. With a concrete understanding of vector geometry, students are able to visualize and understand the meaning of the calculations that they will encounter. By seeing the mathematics and understanding the underlying geometry, students develop mathematical maturity and can think abstractly when they reach vector spaces. Throughout the text, Poole's direct conversational writing style connects with students, and an abundant selection of applications from a broad range of disciplines clearly demonstrates the relevance of linear algebra.

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Product Details

  • ISBN-13: 9780534998455
  • Publisher: Cengage Learning
  • Publication date: 1/24/2005
  • Series: Available Titles CengageNOW Series
  • Edition description: Older Edition
  • Edition number: 2
  • Pages: 736
  • Product dimensions: 7.90 (w) x 9.90 (h) x 1.20 (d)

Meet the Author

David Poole is Professor of Mathematics at Trent University, where he has been a faculty member since 1984. Dr. Poole has won numerous teaching awards: Trent University's Symons Award for Excellence in Teaching (the university's top teaching award), three merit awards for teaching excellence, a 2002 Ontario Confederation of University Faculty Associations Teaching Award (the top university teaching award in the province), a 2003 3M Teaching Fellowship (the top university teaching award in Canada, sponsored by 3M Canada Ltd.), a 2007 Leadership in Faculty Teaching Award from the province of Ontario, and the Canadian Mathematical Society's 2009 Excellence in Teaching Award. From 2002-2007, Dr. Poole was Trent University's Associate Dean (Teaching & Learning). His research interests include discrete mathematics, ring theory, and mathematics education. He received his B.Sc. from Acadia University in 1976 before earning his M.Sc. (1977) and Ph.D. (1984) from McMaster University. When he is not doing mathematics, David Poole enjoys hiking and cooking, and he is an avid film buff.

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Table of Contents

1. VECTORS. Introduction: The Racetrack Game. The Geometry and Algebra of Vectors. Length and Angle: The Dot Product. Exploration: Vectors and Geometry. Lines and Planes. Exploration: The Cross Product. Code Vectors and Modular Arithmetic. Vignette: The Codabar System. Chapter Review. 2. SYSTEMS OF LINEAR EQUATIONS. Introduction: Triviality. Introduction to Systems of Linear Equations. Exploration: Lies My Computer Told Me. Direct Methods for Solving Linear Systems. Exploration: Partial Pivoting. Exploration: Counting Operations - An Introduction to the Analysis of Algorithms. Spanning Sets and Linear Independence. Applications: Allocation of Resources; Balancing Chemical Equations; Network Analysis; Electrical Networks; Finite Linear Games. Vignette: The Global Positioning System. Iterative Methods for Solving Linear Systems. Chapter Review. 3. MATRICES. Introduction: Matrices in Action. Matrix Operations. Matrix Algebra. The Inverse of a Matrix. The LU Factorization. Subspaces, Basis, Dimension, and Rank. Introduction to Linear Transformations. Applications: Markov Chains; Population Growth; Graph Theory; Error-Correcting Codes. Vignette: Robotics. Chapter Review. 4. EIGENVALUES AND EIGENVECTORS. Introduction: A Dynamical System on Graphs. Eigenvalues and Eigenvectors. Determinants. Exploration: Geometric Applications of Determinants. Eigenvalues and Eigenvectors of n x n Matrices. Similarity and Diagonalization. Iterative Methods for Computing Eigenvalues. Applications: Markov Chains; Population Growth; the Perron-Frobenius Theorem; Linear Recurrence Relations; Systems of Linear Differential Equations; Linear Dynamical Systems. Vignette: Ranking Sports Teams and Searching the Internet. Chapter Review. 5. ORTHOGONALITY. Introduction: Shadows on a Wall. Orthogonality in Rn. Orthogonal Complements and Orthogonal Projections. The Gram-Schmidt Process and the QR Factorization. Exploration: The Modified QR Factorization. Exploration: Approximating Eigenvalues with the QR Algorithm. Orthogonal Diagonalization of Symmetric Matrices. Applications: Dual Codes; Quadratic Forms; Graphing Quadratic Forms. Chapter Review. 6. VECTOR SPACES. Introduction: Fibonacci in (Vector) Space. Vector Spaces and Subspaces. Linear Independence, Basis, and Dimension. Exploration: Magic Squares. Change of Basis. Linear Transformations. The Kernel and Range of a Linear Transformation. The Matrix of a Linear Transformation. Exploration: Tilings, Lattices and the Crystallographic Restriction. Applications: Homogeneous Linear Differential Equations; Linear Codes. Chapter Review. 7. DISTANCE AND APPROXIMATION. Introduction: Taxicab Geometry. Inner Product Spaces. Exploration: Vectors and Matrices with Complex Entries. Exploration: Geometric Inequalities and Optimization Problems. Norms and Distance Functions. Least Squares Approximation. The Singular Value Decomposition. Vignette: Digital Image Compression. Applications: Approximation of Functions; Error-Correcting Codes. Chapter Review. Appendix A: Mathematical Notation and Methods of Proof. Appendix B: Mathematical Induction. Appendix C: Complex Numbers. Appendix D: Polynomials.

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Sort by: Showing all of 4 Customer Reviews
  • Posted June 22, 2009

    more from this reviewer

    I Also Recommend:

    Linear Algebra by David Poole is an excellent text for those with advanced mathematical experience and/or skills and provides the reader the opportunity to greatly develop his/her skills in liner algebra analysis.

    This text is one of the best linear algebra texts that I have encountered. However, although the author attempts to organize the material for the student to progress from introductory concepts to the advanced, an understanding of advanced algebra and calculus (vector analysis in 3 dimensions) may be
    needed for success.

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  • Anonymous

    Posted November 15, 2006

    David Poole's Linear Algebra is awesome!!!

    My roommate and I are both taking linear algebra this semester. Same course, different sections, different instructors and - get this - different textbooks! I've got Poole's Linear Algebra and I have to say it beats my roomie's textbook hands down! Poole is easy to read and has lots of helpful examples. Except for needing her book for assigned problems, my roomie uses my copy of Poole for everything else. It's one textbook I don't regret buying.

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  • Anonymous

    Posted July 14, 2006

    The BEST linear algebra book!!

    There are lots of linear algebra books out there so which one should you choose if you have a choice? The one that's easiest to read? Or the one that has great applications? Maybe the one with the best exercises? How about the one that helps you through the theory? Or one that's just plain fun? (Yes, that's not an oxymoron!) Any one of these would be a good reason to choose a textbook but only one book has all of these attributes, in my opinion: Linear Algebra by David Poole. Buy it. You won't be sorry.

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  • Anonymous

    Posted August 18, 2009

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