Linear Algebra

Modules for Interactive Learning Using Maple®

Linear Algebra Modules Project (LAMP), Eugene A. Herman, Michael D. Pepe, Robert T. Moore, James R. King (Autoren)

Media-Kombination

496 Seiten

2000
Pearson
9780201441352 (ISBN)

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A text/CD-ROM package, consisting of 29 Maple learning modules covering the entire introductory linear algebra course as taught at most colleges and universities. The modular structure is designed to permit flexibility in teaching and learning, and to engage students on constructing an understandin

New Interactive Linear Algebra Maple Modules.

Linear Algebra: Modules for Interactive Learning Using Maple 6® is organized into a collection of twenty-nine extensive (and intensive) modules, which must be used in conjunction with Maple 6. Each module is divided into an interactive Tutorial followed by a rich and substantial collection of Problems. Linear Algebra: Modules for Interactive Learning Using Maple 6® has been carefully designed to help students develop their geometric intuition and deepen their understanding of linear algebra concepts and methods.

These modules support both individual work and interactive collaboration. They can be used as a supplement in a traditional lecture course, or in a lab-only format. Due to the versatility of the modules, they can be easily adapted to a variety of curricula, institutions, and styles of teaching.

The modules can be used on all the common hardware platforms—Windows® PCs, Macintosh® computers, and Unix workstations.

1. Systems of Linear Equations.

Module 1. Geometric Perspectives on Linear Equations.

Module 2. Solving Linear Systems Using MAPLE.

Module 3. Some Applications Leading to Linear Systems.

2. Vectors.

Module 1. Geometric Representation of Vectors in the Plane.

Module 2. Linear Combinations of Vectors.

Module 3. Decomposing the Solution of a Linear System.

Module 4. Linear Independence of Vectors.

3. Matrix Algebra.

Module 1. Product of a Matrix and a Vector.

Module 2. Matrix Multiplication.

Module 3. Rules of Matrix Algebra.

Module 4. Markov Chains - An Application.

Module 5. Inverse of a Matrix - An Introduction.

Module 6. Inverse of a Matrix and Elementary Matrices.

Module 7. Determinants.

4. Matrix Transformations.

Module 1. Geometry of Matrix Transformations of the Plane.

Module 2. Geometry of Matrix Transformations of 3-Space.

Module 3. Computer Graphics.

5. Vector Spaces.

Module 1. Subspaces.

Module 2. Basis and Dimension.

Module 3. Subspaces Associated with a Matrix.

Module 4. Loops and Spanning Trees - An Application.

6. Eigenvalues and Eigenvectors.

Module 1. Introduction to Eigenvalues and Eigenvectors.

Module 2. The Characteristic Polynomial.

Module 3. Eigenvector Bases and Discrete Dynamical Systems.

Module 4. Diagonalization and Similarity.

Module 5. Complex Eigenvalues and Eigenvectors.

7. Orthogonality.

Module 1. Orthogonal Vectors and Orthogonal Projections.

Module 2. Orthogonal Bases.

Module 3. Least-Squares Solutions.

Appendix A. Paper and Pencil Tutorial: Gaussian Elimination.

Appendix B. Paper and Pencil Tutorial: Determinants and Cofactors.

Appendix C. The Lamp Library.

Appendix D. Glossary of Linear Algebra Definitions.

Appendix E. List of Linear Algebra Theorems.

Index.

Software Installation Instructions (Windows and Macintosh).

Erscheint lt. Verlag	20.11.2000
Sprache	englisch
Maße	204 x 232 mm
Gewicht	865 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
ISBN-13	9780201441352 / 9780201441352
Zustand	Neuware