MATHEMATICA NOTEBOOKS  FOR MATH 300

The following notebooks were used in class to accompany the lectures listed. Feel free to explore them!

• Section 1.1 -- Systems of Linear Equations

• Section 1.2 -- Row Reduction and Echelon Forms

• Section 1.3 -- Vector Equations

• Section 1.4 -- The Matrix Equation Ax=b

• Section 1.5 -- Solution Sets of Linear Systems

• Section 1.6 -- Applications of Linear Systems

• Section 1.7 -- Linear Independence

• Section 1.8 -- Introduction to Linear Transformations

• Section 1.9 -- The Matrix of a Linear Transformation

• Section 1.10 -- Linear Models in Business, Science, and Engineering
   

• Section 2.1 -- Matrix Operations

• Section 2.2 -- The Inverse of a Matrix

• Section 2.3 -- The Invertible Matrix Theorem

• Section 2.4 -- Partitioned Matrices

• Section 2.5 -- The L-U Decomposition

• Section 2.6 -- The Leontief Input-Output Model

• Section 2.7 -- Applications to Computer Graphics

• Section 2.8 -- Subspaces of Rⁿ

• Section 2.9 -- Dimension and Rank
   

• Section 3.1 -- Definition of the Determinant

• Section 3.2 -- Properties of the Determinant

• Section 3.3 -- Volume and Linear Transformations
   

• Section 4.9 -- Markov Chains

• Section 4.9 -- Markov Chains and Google's PageRank
   

• Section 5.1 -- Eigenvalues and Eigenvectors

• Section 5.2 -- The Characteristic Equation

• Section 5.3 -- Diagonalization

• Section 5.4 -- Eigenvectors and Linear Transformations

• Section 5.5 -- Complex Eigenvalues

• Section 5.6 -- Discrete Dynamical Systems
   

• Section 6.1 -- Inner Product, Length, and Orthogonality

• Section 6.2 -- Orthogonal Sets

• Section 6.3 -- Orthogonal Projections

• Section 6.4 -- The Gram-Schmidt Process and the QR Factorization

• Section 6.5 -- Least-Squares Problems

• Section 6.6 -- Linear Models