Linear Algebra: Modules for Interative Learning Using Maple : Preliminary Version : Updated

by Herman, Eugene A.; Pepe, Michaeld; Moore, Robert T.; King, James R.

• ISBN13: 9780201648461
• ISBN10: 0201648466
• Edition: CD
• Format: Paperback
• Copyright: 1999-08-01
• Publisher: Pearson College Div

Summary

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 ®.

Table of Contents

Systems of Linear Equations	p. 1
Geometric Perspectives on Linear Equations	p. 2
Solving Linear Systems Using MAPLE	p. 12
Some Applications Leading to Linear Systems	p. 24
Vectors	p. 36
Geometric Representation of Vectors in the Plane	p. 37
Linear Combinations of Vectors	p. 48
Decomposing the Solution of a Linear System	p. 63
Linear Independence of Vectors	p. 77
Matrix Algebra	p. 93
Product of a Matrix and a Vector	p. 95
Matrix Multiplication	p. 111
Rules of Matrix Algebra	p. 124
Markov Chains--An Application	p. 134
Inverse of a Matrix--An Introduction	p. 150
Inverse of a Matrix and Elementary Matrices	p. 166
Determinants	p. 176
Matrix Transformations	p. 196
Geometry of Matrix Transformations of the Plane	p. 198
Geometry of Matrix Transformations of 3-Space	p. 225
Computer Graphics	p. 238
Vector Spaces	p. 259
Subspaces	p. 260
Basis and Dimension	p. 268
Subspaces Associated with a Matrix	p. 279
Loops and Spanning Trees--An Application	p. 296
Eigenvalues and Eigenvectors	p. 306
Introduction to Eigenvalues and Eigenvectors	p. 308
The Characteristic Polynomial	p. 326
Eigenvector Bases and Discrete Dynamical Systems	p. 340
Diagonalization and Similarity	p. 360
Complex Eigenvalues and Eigenvectors	p. 380
Orthogonality	p. 408
Orthogonal Vectors and Orthogonal Projections	p. 410
Orthogonal Bases	p. 423
Least-Squares Solutions	p. 438
Paper and Pencil Tutorial: Gaussian Elimination	p. 456
Paper and Pencil Tutorial: Determinants and Cofactors	p. 474
The Lamp Library	p. 481
Glossary of Linear Algebra Definitions	p. 483
List of Linear Algebra Theorems	p. 490
Index	p. 497
Software Installation Instructions (Windows and Macintosh)	p. 501
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