Syllabus
(The
following schedule is subject to changes. Unless specified in the following
notes or in class, all problems listed in department syllabus are assigned.)
1.
Section
1.1: Systems of Linear Equations
Section
1.2: Row reductions & Echelon forms
2.
Section
1.3: Vector Equations
Section
1.4: Matrix Equations Ax=b
3.
Section
1.5: Solution Sets of Linear Systems
Section
1.7: Linear Independence
4.
Section
1.8: Linear Transformations
Section
1.9: The Matrix of a Linear Transformation
5.
Section
2.1: Matrix Operations
Section
2.2: Inverse of a Matrix
Section
2.3: Characterization of Invertible Matrices
6.
Section
3.1: Introduction to Determinants
Section
3.2: Properties of Determinants
������
Midterm Examination I
7.
Section
4.1: Vector Spaces and Subspaces
Section
4.2: Null Space, Column Space, Kernel and Range
8.
Section
4.3: Linear Independent Sets, Bases
Section
4.4: Coordinate Systems
9.
Section
4.5: The Dimension of a Vector Space
10. Section
5.1: Eigenvalues and Eigenvectors
Section
5.2: Characteristic Equations
11. Section
5.3: Diagonalization
Section
6.1: Inner Product, Length and Orthogonality
12. Section
6.2: Orthogonal Sets
Section
6.3: Orthogonal Projections
13. Section
6.4: The Gram-Schmidt Process
Section 6.5. Least-Squares Approximations
Section
6.6 Applications to Linear Models
�������� Midterm Examination II
Course Review for Final
Examination