Description
Apple Academic Press Inc. Exploring Linear Algebra Labs And Projects With Mathematica 2014 Edition by Crista Arangala
Exploring Linear Algebra: Labs and Projects with Mathematica (R) 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 (R) 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 Invertibility Lab 7: Singular or Nonsingular? Why Singularity Matters Lab 8: Mod It Out, Matrices with Entries in ZpLab 9: It's a Complex World Lab 10: Declaring Independence: Is It Linear? Project Set 2 Vector Spaces Lab 11: Vector Spaces and SubspacesLab 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 SpacesLab 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