Exploring Linear Algebra
Labs and Projects with Mathematica ®
Preview
Book Description
Exploring Linear Algebra: Labs and Projects with Mathematica® is a hands-on lab manual for daily use in the classroom. Each lab includes exercises, theorems, and problems that guide your students on an exploration of linear algebra.
The exercises section integrates problems, technology, Mathematica® visualization, and Mathematica CDFs, enabling students to discover the theory and applications of linear algebra in a meaningful way. The theorems and problems section presents the theoretical aspects of linear algebra. Students are encouraged to discover the truth of each theorem and problem, to move toward proving (or disproving) each statement, and to present their results to their peers.
Each chapter also contains a project set consisting of application-driven projects that emphasize the material in the chapter. Students can use these projects as the basis for further undergraduate research.
Table of Contents
Matrix Operations
Lab 0: An Introduction to Mathematica
Lab 1: Matrix Basics and Operations
Lab 2: A Matrix Representation of Linear Systems
Lab 3: Powers, Inverses, and Special Matrices
Lab 4: Graph Theory and Adjacency Matrices
Lab 5: Permutations and Determinants
Lab 6: 4 x 4 Determinants and Beyond
Project Set 1
Invertibility
Lab 7: Singular or Nonsingular? Why Singularity Matters
Lab 8: Mod It Out, Matrices with Entries in Zp
Lab 9: It’s a Complex World
Lab 10: Declaring Independence: Is It Linear?
Project Set 2
Vector Spaces
Lab 11: Vector Spaces and Subspaces
Lab 12: Basing It All on Just a Few Vectors
Lab 13: Linear Transformations
Lab 14: Eigenvalues and Eigenspaces
Lab 15: Markov Chains, An Application of Eigenvalues
Project Set 3
Orthogonality
Lab 16: Inner Product Spaces
Lab 17: The Geometry of Vector and Inner Product Spaces
Lab 18: Orthogonal Matrices, QR Decomposition, and Least Squares Regression
Lab 19: Symmetric Matrices and Quadratic Forms
Project Set 4
Matrix Decomposition with Applications
Lab 20: Singular Value Decomposition (SVD)
Lab 21: Cholesky Decomposition and Its Application to Statistics
Lab 22: Jordan Canonical Form
Project Set 5
Applications to Differential Equations
Lab 23: Linear Differential Equations
Lab 24: Higher-Order Linear Differential Equations
Lab 25: Phase Portraits, Using the Jacobian Matrix to Look Closer at Equilibria
Project Set 6
Mathematica Demonstrations and References
Index
Reviews
"The presented book provides readers with a set of interesting exercises and problems regarding linear algebra. The book covers the scope of an undergraduate course … excellent supplementary material for a linear algebra course …"
—Zentralblatt MATH 1320