MATH 3191:  Applied Linear Algebra  (Fall 2005)
             
Instructor:  Stephen C. Billups
Office:  CU-Denver Bldg., Rm. 607, (303) 556-4814
Office Hours: TR 3-4,  (or by appointment)
 Stephen.Billups@cudenver.edu
www-math.cudenver.edu/~billups/
Overview:  Linear Algebra is one of the most valuable mathematics course many of you will ever take.  In this course, you will learn computational techniques that are essential tools for mathematicians, computer scientists, engineers, economists, and scientists.  But more importantly you will learn important concepts that are fundamental to advanced study in a wide range of fields.  Major topics of the course include solving systems of equations, matrix algebra, determinants, vectors spaces, linear transformations, and applications.

ANNOUNCEMENTS:  

Final Exam will be held on Thursday, Dec. 15, 2005
Tentative Outline:
Day Lecture Topic Sections
Aug. 23 Intro., Systems of Linear Equations 1.1
25 Row Reduction and Echelon Forms 1.2
30 Vector Equations 1.3
Sept. 1 Matrix Equations and Solution Sets 1.4, 1.5
6 Linear Independence 1.7
8 Linear Transformations 1.8, 1.9
13 Matrix Operations 2.1
15 Inverse
 2.2
20 Characterizations of invertible matrices
 2.3
22 Review
27 Exam 1
29
 Determinants, (cont).
 3.1, 3.2
Oct. 4
 Vector Spaces and Subspaces
 4.1
6
 Null Spaces, Column Spaces 4.2
11
 Linearly Independent Sets 4.3
13
 Coordinate Systems, Dimension 4.4, 4.5
18 Rank 4.6
20
 Change of Basis 4.7
25
 Difference Equations
 4.8
27 Review
Nov. 1 Exam 2
3
 Eigenvectors and Eigenvalues, Characteristic Equation
 5.1,5.2
8
 Diagonalization, Eigenvectors and Linear Transformations
 5.3, 5.4
10 Discrete Dynamical Systems 5.6
15 Applications to Differential Equations (if time permits) 5.7
17 Inner Product, Length and Orthogonality 6.1
22 Thanksgiving Break
24 Thanksgiving Break
29
 Orthogonal Sets and Projections 6.2, 6.3
Dec. 1
 Gram-Schmidt Process 6.4
6
 Least-Squares Problems 6.5
8
 Diagonalization of Symmetric Matrices, Quadratic Forms 7.1, 7.2





Last updated: Nov. 9, 2005