MATH 1025 3.0 M  W 2002

APPLIED LINEAR ALGEBRA

  

SYLLABUS (the syllabus is subject to changes announced in class)

 

Polar, Cylindrical and  -Polar Coordinate System
Spherical Coordinates -Polar Coordinate Equations and their Graphs 
-Cylindrical Coordinate System
-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-Decomposition
Eigenvalues, Eigenvectors -Eigenvalues and Eigenvectors
-Diagonalization
-Orthogonal Diagonalization