(Special Offer: Discount 75% of the price)
2nd Edition
David Lay
1999 592
pages (est.) 0201-34774-1 (Paperback)
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 R^n setting, develops them gradually, and returns to them again and
again throughout the text. Finally, when discussed in the abstract, these concepts are
more accessible. Students' conceptual understanding is reinforced through True/False
questions, practice problems, and the use of technology. David Lay changed the face of
linear algebra with the execution of this philosophy, and continues his quest to improve
the way linear algebra is taught with the new Updated Second Edition. With this update, he
builds on this philosophy through increased visualization in the text, vastly enhanced
technology support, and an extensive instructor support package. He has added additional
figures to the text to help students visualize abstract concepts at key points in the
course. A new dedicated CD and Website further enhance the course materials by providing
additional, support to help students gain command of difficult concepts. The CD, included
in the back of the book, contains a wealth of new materials, with a registration coupon
allowing access to a password-protected Website. These new materials are tied directly to
the text, providing a comprehensive package for teaching and learning linear algebra.
Enhanced
visualization for students: additional figures in the margins illustrate graphically
important concepts and procedures.
Icons in the margins flag topics for which expanded or enhanced material is available on
the Website and CD.
CD-ROM. Bundled free with both student and instructor
versions of the text. Includes:
1. Review Sheets and Practice Tests. For student review, these are sample tests with
answer keys and review sheets that highlight important chapter concepts. Written by David
Lay.
2. Downloads. Data files for over 800 excercises in the text - for MATLAB, Maple,
Mathematica, TI-85/86 and HP-48G Calculators.
3. Case Studies. The new case studies are expanded Introductory Examples that frame the
existing situation or problem, adding applicable real-world data and referencing material
in the text. Refer to Table of Contents for topics covered.
4. New Applications. These are projects, problems, and applications exercises based on
real-world data and keyed to the text. They are challenging and require the use of
graphing technology. New applications also include challenging Problems. These are more
in-depth problems that supplement those already in the text. These problems may or may not
require graphing technology. Instructors now have a selection of more challenging problems
to further expand the ideas in the book.
5. References to Applications. This is a list of the areas from which applications in the
text are drawn. Color icons take users directly to relevant material on the CD and
Website.
6. Study Guide Sample. This sample from Chapter 1 of the supplemental Study Guide
demonstrates to students the importance of this resource.
Student Website. Accessible via password bundled with the Student Edition. Contains
everything on the CD, plus:
7. Related Linear Algebra Links. These links to other Websites of interest to instructors
and students are included to allow for further discovery. Data sources, applications of
linear algebra, and other math-related sites are among the many links supplied.
Instructor Website. Accessible ONLY to instructors via password. Contains everything on
the CD and Student Website, plus:
8. Transparency Masters. This is a comprehensive package including key figures from the
text to aid in visualization, as well as text-based slides with additional numerical
examples and summaries of key ideas. These materials contain coverage for every chapter in
the text.
9. Sample Syllabi. This contains five possible "paths" through the text to
reflect different teaching goals and prerequisites. Written by David Lay.
10. Sample Tests. Additional sample tests, review sheets, and answer keys written by David
Lay.
Continued Features of the text.
Fundamental ideas of linear algebra introduced within the first seven lectures, in the
concrete setting of R^n, and then gradually examined from different points of view. Later
generalizations of these concepts appear as natural extensions of familiar ideas.
A modern view of matrix multiplication. Definitions and proofs focus on the columns of a
matrix rather than on the matrix entries.
Numerical Notes. These 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-85, TI-86, and HP-48G. Data for these exercises are
provided on the Website: http://www.laylinalgebra.com.
Section 2.9 is optional, which permits instructors to cover eigenvalues very early, by
omitting or postponing Chapters 3 and 4.
(Each
chapter begins with an Introductory Example and
ends with Supplementary Exercises.) 1. Linear Equations In Linear Algebra.
Systems of Linear Equations.
Row Reduction and Echelon Forms.
Vector Equations.
The Matrix Equation ax = b.
Solution Sets of Linear Systems.
Linear Independence.
Introduction to Linear Transformations.
The Matrix of a Linear Transformation.
Linear Models in Business, Science, and Engineering.
2. Matrix Algebra.
Matrix Operations.
The Inverse of a Matrix.
Characterizations of Invertible Matrices.
Partitioned Matrices.
Matrix Factorizations.
Iterative Solutions of Linear Systems.
The Leontief Input-Output Model.
Applications to Computer Graphics.
Subspaces of R^n.
3. Determinants.
Introduction to Determinants.
Properties of Determinants.
Cramer's Rule, Volume, and Linear Transformations.
4. Vector Spaces.
Vector Spaces and Subspaces.
Null Spaces, Column Spaces, and Linear Transformations.
Linearly Independent Sets; Bases.
Coordinate Systems.
The Dimension of a Vector Space.
Rank.
Change of Basis.
Applications to Difference Equations.
Applications to Markov Chains.
5. Eigenvalues and Eigenvectors.
Eigenvectors and Eigenvalues.
The Characteristic Equation.
Diagonalization.
Eigenvectors and Linear Transformations.
Complex Eigenvalues.
Discrete Dynamical Systems.
Applications to Differential Equations.
Iterative Estimates for Eigenvalues.
6. Orthogonality and Least-Squares.
Inner Product, Length, and Orthogonality.
Orthogonal Sets.
Orthogonal Projections.
The Gram-Schmidt Process.
Least-Squares Problems.
Applications to Linear Models.
Inner Product Spaces.
Applications of Inner Product Spaces.
7. Symmetric Matrices and Quadratic Forms.
Diagonalization of Symmetric Matrices.
Quadratic Forms.
Constrained Optimization.
The Singular Value Decomposition.
Applications to Image Processing and Statistics.
Appendices.
Uniqueness of the Reduced Echelon Form.
Complex Numbers.
