Linear Algebra: Modules for Interactive Learning Using Maple 6

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

• ISBN13: 9780201441352
• ISBN10: 0201441357
• Edition: CD
• Format: Paperback
• Copyright: 2000-11-01
• Publisher: Pearson College Div

Summary

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 platformsWindows? PCs, Macintosh? computers, and Unix workstations.

Table of Contents

Systems of Linear Equations	1	(35)
Geometric Perspectives on Linear Equations	2	(10)
Solving Linear System's Using MAPLE	12	(12)
Some Applications Leading to Linear Systems	24	(12)
Vectors	36	(57)
Geometric Representation of Vectors in the Plane	37	(11)
Linear Combinations of Vectors	48	(15)
Decomposing the Solution of a Linear System	63	(14)
Linear Independence of Vectors	77	(16)
Matrix Algebra	93	(103)
Product of a Matrix and a Vector	95	(16)
Matrix Multiplication	111	(13)
Rules of Matrix Algebra	124	(10)
Markov Chains --- An Application	134	(16)
Inverse of a Matrix --- An Introduction	150	(16)
Inverse of a Matrix and Elementary Matrices	166	(10)
Determinants	176	(20)
Matrix Transformations	196	(63)
Geometry of Matrix Transformations of the Plane	198	(27)
Geometry of Matrix Transformations of 3-Space	225	(13)
Computer Graphics	238	(21)
Vector Spaces	259	(47)
Subspaces	260	(8)
Basis and Dimension	268	(11)
Subspaces Associated with a Matrix	279	(17)
Loops and Spanning Trees --- An Application	296	(10)
Eigenvalues and Eigenvectors	306	(102)
Introduction to Eigenvalues and Eigenvectors	308	(18)
The Characteristic Polynomial	326	(14)
Eigenvector Bases and Discrete Dynamical Systems	340	(20)
Diagonalization and Similarity	360	(20)
Complex Eigenvalues and Eigenvectors	380	(28)
Orthogonality	408	(48)
Orthogonal Vectors and Orthogonal Projections	410	(13)
Orthogonal Bases	423	(15)
Least-Squares Solutions	438	(18)
Appendix A. Paper and Pencil Tutorial: Gaussian Elimination	456	(18)
Appendix B. Paper and Pencil Tutorial: Determinants and Cofactors	474	(7)
Appendix C. The Lamp Library	481	(2)
Appendix D. Glossary of Linear Algebra Definitions	483	(7)
Appendix E. List of Linear Algebra Theorems	490	(7)
Index	497	(4)
Software Installation Instructions (Windows and Macintosh)	501