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Linear Algebra and Its Applications with CD-ROM, Update, 3/E
David C. Lay, University of Maryland

ISBN-10: 0321287134
ISBN-13: 9780321287137

Publisher: Addison-Wesley
Copyright: 2006
Format: Cloth Bound w/CD-ROM; 576 pp
Published: 08/22/2005

Suggested retail price: $141.33
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Linear algebra is relatively easy for students during the early stages of the course, when the material is presented in a familiar, concrete setting. But when abstract concepts are introduced, students often hit a brick wall. Instructors seem to agree that certain concepts (such as linear independence, spanning, subspace, vector space, and linear transformations), are not easily understood, and require time to assimilate. Since they are fundamental to the study of linear algebra, students' understanding of these concepts is vital to their mastery of the subject. Lay introduces these concepts early in a familiar, concrete Rn setting, develops them gradually, and returns to them again and again throughout the text so that when discussed in the abstract, these concepts are more accessible.



 

  • MyMathLab:

      • For Instructors:

      o        Homework and test managers

      o        Compatible with TestGen® tests

      o        Online grade book

       

      For Students:

      o        Review sheets and Practice Tests to help students prepare for exams.

      o        Integrated Excerpts from the Study Guide

      o        The Lay Linear Algebra textbook in a multimedia format.

       

      • Fundamental ideas of linear algebra are introduced within the first seven lectures, in the concrete setting of Rn, and then gradually examined from different points of view. Later generalizations of these concepts appear as natural extensions of familiar ideas.
      • Focus on visualization of concepts throughout the book.
      • Icons in the margins to flag topics for which expanded or enhanced material is available on the Web via MyMathLab.
      • A modern view of matrix multiplication is presented. Definitions and proofs focus on the columns of a matrix rather than on the matrix entries.
      • Numerical Notes give a realistic flavor to the text. Students are reminded frequently of issues that arise in the real-life use of linear algebra.
      • Each major concept in the course is given a geometric interpretation because many students learn better when they can visualize an idea.
      • [M] exercises appear in every section. To be solved with the aid of a [M]atrix program such as MATLAB™, Maple®, Mathematica®, MathCad®, Derive® or programmable calculators with matrix capabilities, such as the TI-83 Plus®, TI-86®, TI-89®, and HP-48G®. Data for these exercises are provided on the Web.

       

      • New Chapters!  (Chapter 8: The Geometry of Vector Spaces and Chapter 9: Optimization) available on the web via MyMathLab.
      • Easily identifiable CD icons in the margins reference exploratory MATLAB projects that are available on the CD-ROM bound in new copies of the book.
      • Study Guide Icons point out concepts that are expanded on in the Study Guide (available in print and on the CD-ROM bound in all new copies of the book) helping students master concepts.
      • CD-Rom bound in the back of the book includes: the entire Study Guide, Getting Started Introductions on Technology use, and additional MATLAB projects.

       

      Chapter 1  Linear Equations in Linear Algebra

       

      INTRODUCTORY EXAMPLE: Linear Models in Economics and Engineering

       

      1.1                   Systems of Linear Equations

      1.2                   Row Reduction and Echelon Forms

      1.3                   Vector Equations

      1.4                   The Matrix Equation Ax = b

      1.5                   Solution Sets of Linear Systems

      1.6                   Applications of Linear Systems

      1.7                   Linear Independence

      1.8                   Introduction to Linear Transformations

      1.9                   The Matrix of a Linear Transformation

      1.10                 Linear Models in Business, Science, and Engineering

              Supplementary Exercises

       

      Chapter 2  Matrix Algebra

       

      INTRODUCTORY EXAMPLE: Computer Models in Aircraft Design

       

      2.1                   Matrix Operations

      2.2                   The Inverse of a Matrix

      2.3                   Characterizations of Invertible Matrices

      2.4                   Partitioned Matrices

      2.5                   Matrix Factorizations

      2.6                   The Leontief Input=Output Model

      2.7                   Applications to Computer Graphics

      2.8                   Subspaces of R^n

      2.9                   Dimension and Rank

              Supplementary Exercises

       

      Chapter 3  Determinants

       

      INTRODUCTORY EXAMPLE: Determinants in Analytic Geometry

       

      3.1                   Introduction to Determinants

      3.2                   Properties of Determinants

      3.3                   Cramer’s Rule, Volume, and Linear Transformations

              Supplementary Exercises

       

      Chapter 4  Vector Spaces

       

      INTRODUCTORY EXAMPLE: Space Flight and Control Systems

       

      4.1                   Vector Spaces and Subspaces

      4.2                   Null Spaces, Column Spaces, and Linear Transformations

      4.3                   Linearly Independent Sets; Bases

      4.4                   Coordinate Systems

      4.5                   The Dimension of a Vector Space

      4.6                   Rank

      4.7                   Change of Basis

      4.8                   Applications to Difference Equations

      4.9                   Applications to Markov Chains

              Supplementary Exercises

       

      Chapter 5  Eigenvalues and Eigenvectors

       

      INTRODUCTORY EXAMPLE: Dynamical Systems and Spotted Owls

       

      5.1                   Eigenvectors and Eigenvalues

      5.2                   The Characteristic Equation

      5.3                   Diagonalization

      5.4                   Eigenvectors and Linear Transformations

      5.5                   Complex Eigenvalues

      5.6                   Discrete Dynamical Systems

      5.7                   Applications to Differential Equations

      5.8                   Iterative Estimates for Eigenvalues

              Supplementary Exercises

       

      Chapter 6  Orthogonality and Least Squares

       

      INTRODUCTORY EXAMPLE: Readjusting the North American Datum

       

      6.1                   Inner Product, Length, and Orthogonality

      6.2                   Orthogonal Sets

      6.3                   Orthogonal Projections

      6.4                   The Gram-Schmidt Process

      6.5                   Least-Squares Problems

      6.6                   Applications to Linear Models

      6.7                   Inner Product Spaces

      6.8                   Applications of Inner Product Spaces

              Supplementary Exercises

       

      Chapter 7  Symmetric Matrices and Quadratic Forms

       

      INTRODUCTORY EXAMPLE: Multichannel Image Processing

       

      7.1                   Diagonalization of Symmetric Matrices

      7.2                   Quadratic Forms

      7.3                   Constrained Optimization

      7.4                   The Singular Value Decomposition

      7.5                   Applications to Image Processing and Statistics

              Supplementary Exercises

       

      ONLINE ONLY Chapter 8  The Geometry of Vector Spaces

       

      INTRODUCTORY EXAMPLE: The Platonic Solids

       

      8.1                   Affine Combinations

      8.2                   Affine Independence

      8.3                   Convex Combinations

      8.4                   Hyperplanes

      8.5                   Polytopes

      8.6                   Curves and Surfaces

              Supplementary Exercises

       

      ONLINE ONLY Chapter 9  Optimization

       

      INTRODUCTORY EXAMPLE: The Berlin Airlift

       

      9.1                    Matrix Games

      9.2                    Linear Programming — Geometric Method

      9.3              Linear Programming — Simplex Method

      9.4              Duality

              Supplementary Exercises

       

       

       

      Appendices

       

      A                    Uniqueness of the Reduced Echelon Form

      B                    Complex Numbers

       

      Glossary

       

      Answers to Odd-Numbered Exercises

       

      Index

      David C. Lay holds a B.A. from Aurora University (Illinois), and an M.A. and Ph.D. from the University of California at Los Angeles. Lay has been an educator and research mathematician since 1966, mostly at the University of Maryland, College Park. He has also served as a visiting professor at the University of Amsterdam, the Free University in Amsterdam, and the University of Kaiserslautern, Germany. He has over 30 research articles published in functional analysis and linear algebra.

      As a founding member of the NSF-sponsored Linear Algebra Curriculum Study Group, Lay has been a leader in the current movement to modernize the linear algebra curriculum. Lay is also co-author of several mathematics texts, including Introduction to Functional Analysis, with Angus E. Taylor, Calculus and Its Applications, with L.J. Goldstein and D.I. Schneider, and Linear Algebra Gems-Assets for Undergraduate Mathematics, with D. Carlson, C.R. Johnson, and A.D. Porter.

      A top-notch educator, Professor Lay has received four university awards for teaching excellence, including, in 1996, the title of Distinguished Scholar-Teacher of the University of Maryland. In 1994, he was given one of the Mathematical Association of America's Awards for Distinguished College or Unviersity Teaching of Mathematics. He has been elected by the university students to membership in Alpha Lambda Delta National Scholastic Honor Society and Golden Key National Honor Society. In 1989, Aurora University conferred on him the Outstanding Alumnus award. Lay is a member of the American Mathematical Society, the Canadian Mathematical Society, the International Linear Algebra Society, the Mathematical Association of America, Sigma Xi, and the Society for Industrial and Applied Mathematics. Since 1992, he has served several terms on the national board of the Association of Christians in the Mathematical Sciences.

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