Notes for Math 227

1.   Vectors and Vector Operations
  1.1   Types of Vectors
  1.2   Vector Operations
  1.3   Linear Functions
  1.4   Multiplication of Vectors
  1.5   Vector operations in Mathematica


2.   Matrices and Matrix Operations
  2.1   Matrices, addition, subtraction  and multiplication bv a number
  2.2   Multiplication of Vectors by Matrices - Linear Functions
  2.3   Multiplication of Matrices
  2.4   Geometric Transformations
  2.5   Matrix operations in Mathematica
  2.6   Vector & matrix operations in MATLAB

3.   Linear Equations
  3.1   Gaussian Elimination
  3.2   Fitting Equations to Data
  3.3   More Unknowns than Equations
  3.4   Electrical Networks
  3.5   Uniqueness of Solutions to Linear Equations - Linear Independence & Dependence
  3.6   Existence of solutions to linear equations
  3.7   Solving equations in Mathematica
  3.8   Solving equations & matrix inverses in MATLAB 
  3.9   Plotting Data and Equations on the Same Graph

4.	Inverses of Matrices
  4.1   Inverses of Matrices
  4.2   Algebraic Properties of Inverses
  4.3   Leontif Input-Output Models
  4.4   Finding Inverses with Mathematica

5.	Determinants
  5.1   Definition of Determinants
  5.2   Properties of Determinants
  5.3   Applications of Determinants
  5.4   Finding Determinants with Mathematica
    
6.	Eigenvalues and Eigenvectors
  6.1   Computing Eigenvalues and Eigenvectors
  6.2   Complex Eigenvalues
  6.3   Diagonalization & Matrix Powers  
  6.4   Difference Equations  
  6.5   Diagonalization of Matices with Complex Eigenvalues 
  6.6   Eigenvalues & eigenvectors in Mathematica
  6.7   Eigenvalues & eigenvectors in MATLAB  

7.	Orthogonal Projection and Least Squares
  7.1   Projection on a Line
  7.2   Projection on a Plane

8.	Symmetric Matrices and Quadratic Functions
  8.1   Symmetric Matrices
  8.2   Orthogonal Matrices
  8.3   Quadratic Functions

9.	Subspaces and Bases
  9.1   Subspaces
  9.2   Coordinate Systems and Bases
  
10.	Eigenvalues of Multiplicy Greater Than One
  10.1   Diagonalizable Matrices
  10.2   Generalized Eigenvectors

11.  An Introduction to Mathematica

  Mathematics 227 Directory