

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 2space and 3space 
 Introduction
to Vectors (Geometric) 


 Norm of
a Vector; Vector Arithmetic 


 Dot Product;
Projections 


 Cross Product 


 Lines and
Planes in 3space 




Euclidean
Vectors Spaces 
 Euclidean
nSpace 


 Linear
Transformations from R^{n} to R^{m} 


 Properties
of Linear Transformations from R^{n} to R^{m} 




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; GramSchmidt Process; QRDecopmosition 




Eigenvalues,
Eigenvectors 
 Eigenvalues
and Eigenvectors 


 Diagonalization 


 Orthogonal
Diagonalization 



