Linear algebra : an interactive approach
Author(s)
Bibliographic Information
Linear algebra : an interactive approach
Thomson Brooks/Cole, c2004
Student ed
- CD-ROM
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Note
System requirements for accompanying CD-ROM: Microsoft Windows 98 and higher
Includes index
Description and Table of Contents
- Volume
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ISBN 9780534409159
Description
Utilizing technology to enrich the learning experience, S.K. Jain and A.D. Gunawardena provide an exciting introduction to linear algebra. The accompanying CD-ROM contains the entire contents of the book in a searchable format. The CD-ROM also includes MATLAB drills, concept demonstrations, solutions, projects, and chapter tests. In addition to the CD-ROM, the Web site contains additional problems, projects, and applications, as well as support for MAPLE and Mathematica. In the book, the authors introduce matrices as a handy tool for solving systems of linear equations and then demonstrate that their utility goes far beyond this initial application. Students discover that hardly any area of modern mathematics exists where matrices do not have some application. Offering flexibility in the approach, this book can be used in a traditional course without technology or in a course using technology.
Table of Contents
1. LINEAR SYSTEMS AND MATRICES.
Linear Systems of Equations. Elementary Operations and Gauss Elimination Method. Homogeneous Linear Systems. Introduction to Matrices and the Matrix of a Linear System. Elementary Row Operations on a Matrix. Proofs of Facts. Chapter Review Questions and Project.
2. ALGEBRA OF MATRICES.
Scalar Multiplication and Addition of Matrices. Matrix Multiplication and its Properties. Transpose. Proofs of Facts. Chapter Review Questions and Projects.
3. SUBSPACES.
Linear Combination of Vectors. Vector Subspaces. Linear Dependence, Linear Independence and Basis. Proofs of Facts. Chapter Review Questions and Project.
4. RANK.
Elementary Operations and Rank. Null Space and Nullity of a Matrix. Elementary Matrices. Proofs of Facts. Chapter Review Questions and Project.
5. INVERSE, RANK FACTORIZATION, AND LU-DECOMPOSITION.
Inverse of a Matrix and Its Properties. Further Properties of Inverses. Full-Rank Factorization. LU-Decomposition of a Matrix. Proofs of Facts. Chapter Review Questions and Projects.
6. DETERMINANTS.
Determinant. Properties of the Determinant. Cofactors and Inverse of a Matrix. Cramer''s Rule. Chapter Review Questions and Projects.
7. EIGENVALUE PROBLEMS.
Eigenvalues and Eigenvectors. Characteristic Polynomial. Calculating Eigenvalues and Eigenvectors (Another Approach) and the Cayley-Hamilton. Applications of the Cayley-Hamilton Theorem/ Properties of Eigenvalues, Diagonalizability, and Triangularizability. Proofs and Facts. Chapter Review Questions and Project.
8. INNER PRODUCT SPACES.
Gram-Schmidt Orthogonalization Process. Diagonalization of Symmetric Matrices. Application of the Spectral Theorem. Least-Squares Solution. Generalized Inverse and Least-Squares Solution. Proofs and Facts. Chapter Review Questions and Projects.
9. VECTOR SPACES AND LINEAR MAPPINGS.
Vector Spaces. Linear Dependence and Linear Independence. Linear Mappings. Some Properties of Linear Mappings:Image and Kernel. Linear Mappings and Matrices. Chapter Review Questions and Project.
10. DETERMINANTS (REVISITED).
Permutations. Determinants. Cofactor Expansion. Adjoint of a Matrix. Cramer''s Rule. Product Theorem of Determinants.
Answers and Hints to Selected Exercises.
Drill Solutions Using Matlab.
Some Basic Matlab Operations.
Index.
- Volume
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CD-ROM ISBN 9780534420888
Description
AUTOMATICALLY PACKAGED WITH EVERY NEW COPY OF THE BOOK AND NOT AVAILABLE SEPARATELY, this accompanying Interactive CD contains some striking features. The software allows instructors to customize this linear algebra textbook to suit their course by tightly integrating instructor-developed material with the textbook content. Instructors using this text will be able to add course related content (Power Point lecture notes, MS Word or pdf files, Web pages etc.) exactly where they belong in the textbook. For example, using the software tool kit, instructor can easily build a learning profile by highlighting, annotating textbook sections, adding relevant files or web links to create a comprehensive guided tour of the textbook content. This profile then can be shared with all or some of the students using email. The static content in the CD is organized in a pedagogically meaningful way by connecting linear algebra concepts demos, MATLAB exercises, and references in the text. MATLAB exercises are carefully linked to the appropriate discussion in the text so the user can solve problems easily by referring to worked examples. There is an abundance of worked examples and exercises provided to improve the understanding of material. Also, electronic copy of the text allows highlighting, book marking pages, adding annotations, or adding any other link (such as a web page) directly into the text. This fully interactive electronic text combines a highly effective pedagogical design with powerful tools of modern e-learning technology.
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