Polar Coordinates -  The Polar Coordinate System
-  Polar Coordinate Equations and their Graphs 
-  The Cylindrical Coordinate System
-  The Spherical Coordinate System
Complex Numbers  -  Complex Numbers in Standard Form
-  Operations on Complex Numbers in Standard Form
-  Polar Form of a Complex Number
-  Finding Powers and Roots of Complex Numbers
Systems of Linear Equations - Gaussian Elimination
- Matrices and Matrix Operations
- Inverses; Rules of Matrix Arithmetic
- Elementary Matrices and Method for Finding A-1
- Further Results on Systems of Equations and Invertibility
- Diagonal, Triangular, and Symmetric Matrices
 
Determinants  - Evaluating Determinants by Row Reduction
- Properties of the Determinant Function
- Cofactor Expansion; Cramer's Rule
   
Vectors in 2-space and 3-space - Introduction to Vectors (Geometric)
- Norm of a Vector; Vector Arithmetic
- Dot Product; Projections
- Cross Product
- Lines and Planes in 3-space
Euclidean Vectors Spaces - Euclidean n-Space
- Linear Transformations from Rn to Rm
- Properties of Linear Transformations from Rn to Rm
General Vector Spaces - Real Vector Spaces
- Subspaces
- Linear Independence
- Basis and Dimension
- Row Space, Column Space, Nullspace
- Rank and Nulllity
   
Inner Product Spaces - Orthonormal Bases; Gram-Schmidt Process; QR-Decopmosition
Eigenvalues, Eigenvectors - Eigenvalues and Eigenvectors
- Diagonalization
- Orthogonal Diagonalization