1st Edition

Exploring Linear Algebra Labs and Projects with Mathematica ®

By Crista Arangala Copyright 2015
    152 Pages 38 B/W Illustrations
    by Chapman & Hall

    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.

    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

    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

    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



    Crista Arangala

    "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