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Linear Algebra and Its Applications with CD-ROM, Update, 3/E
ISBN-10: 0321287134
ISBN-13: 9780321287137
Publisher: Pearson
Copyright: 2006
Format: Cloth Bound w/CD-ROM; 576 pp
Published: 08/22/2005
Status: Instock
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.
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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ISBN-10: 0201721708 |
ISBN-13: 9780201721706
MyMathLab Online Course Update, 3/E
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ISBN-13: 9780321280619
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ISBN-10: 0321369610 |
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Instructor's Edition Update, 3/E
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©2006 | Pearson | Cloth Bound w/CD-ROM; 660 pp | Instock
ISBN-10: 0321280636 |
ISBN-13: 9780321280633
Chapter 8 for Instructor Resource CD Update, 3/E
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©2006 | Pearson | On-line Supplement | Instock
ISBN-10: 0321409795 |
ISBN-13: 9780321409799
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Chapter 9 for Instructor Resource CD Update, 3/E
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ISBN-10: 0321409809 |
ISBN-13: 9780321409805
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Companion Website Update, 3/E
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ISBN-10: 0321369610 |
ISBN-13: 9780321369611
HP Manual Update, 3/E
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©2006 | Pearson | Paper; 50 pp | Instock
ISBN-10: 0321280709 |
ISBN-13: 9780321280701
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Instructor's Maple® Manual for Linear Algebra and Its Applications Update, 3/E
Meade
©2008 | Pearson | Paper; 80 pp | Instock
ISBN-10: 0321388860 |
ISBN-13: 9780321388865
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Instructor's Solutions Manual (Download only) for Linear Algebra and Its Applications, Update, 3/E
Lay & Polaski
©2006 | Pearson | On-line Supplement; 424 pp | Out of Stock
ISBN-10: 0321280652 |
ISBN-13: 9780321280657
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Maple Manual Update, 3/E
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ISBN-10: 0321280644 |
ISBN-13: 9780321280640
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ISBN-10: 0321280687 |
ISBN-13: 9780321280688
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Matlab Manual Update, 3/E
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ISBN-10: 0321280695 |
ISBN-13: 9780321280695
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ISBN-13: 9780321280619
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TI Manual Update, 3/E
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©2006 | Pearson | Paper; 100 pp | Instock
ISBN-10: 0321305183 |
ISBN-13: 9780321305183
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©2006 | Pearson | On-line Supplement | Instock
ISBN-10: 0321280601 |
ISBN-13: 9780321280602
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Transparencies, Sample Syllabi, Review Sheets, Practice Exams for Linear Algebra and Its Applications, Update, 3/E
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©2006 | Pearson | On-line Supplement | Instock
ISBN-10: 0321395948 |
ISBN-13: 9780321395948
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Companion Website Update, 3/E
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ISBN-10: 0321369610 |
ISBN-13: 9780321369611
MathXL Digital Student Access Code (12-month)
Addison-Wesley
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ISBN-10: 0321488652 |
ISBN-13: 9780321488657
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ISBN-10: 032128061X |
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ISBN-10: 0321280660 |
ISBN-13: 9780321280664
For Introductory Linear Algebra
Understanding Linear Algebra Using MATLAB
Kleinfeld & Kleinfeld
©2001 | Pearson | Paper; 210 pp | Out of Stock
ISBN-10: 0130609455 |
ISBN-13: 9780130609458
Visualizing Linear Algebra Using Maple
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ISBN-10: 0130418161 |
ISBN-13: 9780130418166
Addison-Wesley's Algebra Review
Addison-Wesley
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ISBN-10: 0321247086 |
ISBN-13: 9780321247087
Addison-Wesley's Basic Math Review
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ISBN-10: 0321247078 |
ISBN-13: 9780321247070
Algebra Review Study Card, 2/E
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ISBN-13: 9780321394736
Allied Health Study Card, 2/E
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Basic Math Review Card, 2/E
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ISBN-13: 9780321394767
Concept Videos: Algebra
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ISBN-10: 0321517199 |
ISBN-13: 9780321517197
Concept Videos: Basic Math & Prealgebra
Addison-Wesley
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ISBN-10: 032151758X |
ISBN-13: 9780321517586
Discovering Algebra: Examples with Keystrokes on the TI-83/TI-82 and TI-85/TI-86, A Laboratory Approach
Pirich & Bigliani
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ISBN-10: 0136492037 |
ISBN-13: 9780136492030
Finite Mathematics Study Card
Addison-Wesley
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ISBN-10: 0321374398 |
ISBN-13: 9780321374394
Flash Review Series: Algebra
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ISBN-13: 9780321143099
Graphing Calculator Reference Card, 3/E
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ISBN-10: 0321394755 |
ISBN-13: 9780321394750
Graphing Calculator Tutorial CD
Addison-Wesley
©2006 | Pearson | CD-ROM Only | Instock
ISBN-10: 0321357744 |
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Math for Allied Health Study/Reference Card
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ISBN-10: 0321336542 |
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Mathematics Spanish Glossary, 2/E
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Overcoming Math Anxiety, 2/E
Davidson & Levitov
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ISBN-10: 0321069188 |
ISBN-13: 9780321069184
Pearson TI Rebate Coupon $15, 2/E
Pearson
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ISBN-10: 0321566041 |
ISBN-13: 9780321566041
Prealgebra Review Workbook
Wheel
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ISBN-10: 0321473329 |
ISBN-13: 9780321473325
Review of Algebra, A
Howard
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ISBN-10: 0201773473 |
ISBN-13: 9780201773477
Saleable Technology Bundle, 2/E
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ISBN-13: 9780321280619
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