Linear Algebra

Modules for Interactive Learning Using Maple (LAMP)

Eugene A. Herman, Michael D. Pepe, Robert T. Moore, James R. King (Autoren)

Media-Kombination

326 Seiten

1999
Pearson
9780201648461 (ISBN)

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DESCRIPTION Linear Algebra: Modules for Interactive Learning Using Maple® is organized into a collection of twenty-eight extensive (and intensive) modules, which must be used in conjunction with Release 5 of Maple V®. 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® 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 their versatility, they can be easily adapted to a variety of curricula, institutions, and styles of teaching. Goals of the Modules 1. To help students develop their geometric intuition about the concepts of linear algebra; 2. To deepen students' understanding of the algebraic formulation of these concepts and to strengthen their ability to manipulate concepts; 3. To help students gain an appreciation of how the concepts and methods of linear algebra are applied. Structure of the Modules Each module is divided into two main parts, the Tutorial and the Problems: The Tutorial is further divided into sections and consists of an interlaced text (usually brief), examples and demonstrations, and exercises (with answers provided in closed sections). The Problems are all intended to be fairly substantial, as they provide the work on which students will be graded. They include explorations, applications, constructions (e.g., of specified types of matrices or specified pictures or animations), counter-examples, short essays, proofs, true/false questions, and many challenging computations. Each module is a Maple worksheet that is to be used in conjunction with Release 5 of Maple V ®.

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. Linear 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. Eigenspaces and Eigenvector Bases.

Module 3. Eigenvector Analysis of Discrete Dynamical Systems.

Module 4. Diagonalization and Similarity.

7. Orthogonality.

Module 1. Orthogonal Vectors and Orthogonal Projections.

Module 2. Orthogonal Bases.

Module 3. Least Squares Solutions.

Software Installation Instructions - Macintosh.

Software Installation Instructions - Windows.

Erscheint lt. Verlag	29.9.1999
Sprache	englisch
Maße	216 x 279 mm
Gewicht	815 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
ISBN-13	9780201648461 / 9780201648461
Zustand	Neuware