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Linear Algebra and Its Applicationsby David C. Lay
Synopses & ReviewsPublisher Comments:ALERT: Before you purchase, check with your instructor or review your course syllabus to ensure that you select the correct ISBN. Several versions of Pearson's MyLab & Mastering products exist for each title, including customized versions for individual schools, and registrations are not transferable. In addition, you may need a CourseID, provided by your instructor, to register for and use Pearson's MyLab & Mastering products.
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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. David Lay introduces these concepts early in a familiar, concrete R^{n} 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.
NEW! MyMathLab is now available for this text. The course features hundreds of assignable homework exercises plus the complete eBook, in addition to its wide range of tutorial and assessment tools that make it easy to manage your course online. Synopsis:This package contains:
0321262522: MyMathLab — Valuepack Access Card 0321385179: Linear Algebra and Its Applications 0321388836: Student Study Guide for Linear Algebra and Its Applications Synopsis:0321791541 / 9780321791542 Linear Algebra and Its Applications with Student Study Guide
Package consists of: 0321385179 / 9780321385178 Linear Algebra and Its Applications 0321388836 / 9780321388834 Student Study Guide for Linear Algebra and Its Applications About the AuthorDavid 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 NSFsponsored Linear Algebra Curriculum Study Group, Lay has been a leader in the current movement to modernize the linear algebra curriculum. Lay is also coauthor 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 GemsAssets for Undergraduate Mathematics, with D. Carlson, C.R. Johnson, and A.D. Porter. Professor Lay has received four university awards for teaching excellence, including, in 1996, the title of Distinguished ScholarTeacher of the University of Maryland. In 1994, he was given one of the Mathematical Association of America's Awards for Distinguished College or University 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. Table of Contents1. 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
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
3. Determinants Introductory Example: Random Paths and Distortion 3.1 Introduction to Determinants 3.2 Properties of Determinants 3.3 Cramer’s Rule, Volume, and Linear Transformations Supplementary Exercises
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
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
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 LeastSquares Problems 6.6 Applications to Linear Models 6.7 Inner Product Spaces 6.8 Applications of Inner Product Spaces Supplementary Exercises
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
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
9. Optimization (Online Only) Introductory Example: The Berlin Airlift 9.1 Matrix Games 9.2 Linear Programming–Geometric Method 9.3 Linear Programming–Simplex Method 9.4 Duality
10. FiniteState Markov Chains (Online Only) Introductory Example: Google and Markov Chains 10.1 Introduction and Examples 10.2 The SteadyState Vector and Google's PageRank 10.3 FiniteState Markov Chains 10.4 Classification of States and Periodicity 10.5 The Fundamental Matrix 10.6 Markov Chains and Baseball Statistics
Appendices A. Uniqueness of the Reduced Echelon Form B. Complex Numbers What Our Readers Are SayingBe the first to add a comment for a chance to win!Product Details
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