Math 351 - Fall 2007 - Course Outline

All section numbers refer to Otto Bretscher's "Linear Algebra with Applications", 3rd edition.

WeekReading Topics
1   (8/29 - 8/31) Appendix A
      1.1
      1.2		 Vectors
Introduction to linear systems
Matrices and Gauss-Jordan elimination
2   (9/3 - 9/7)       1.3
      2.1
      2.2 		On the solutions of linear systems
Intro to linear transformation
Linear transformations in geometry
3   (9/10 - 9/14)       2.3
      2.4 		Inverse of a linear transformation
Matrix products
4   (9/17 - 9/19)       3.1
      ..
 Image and kernel of a linear transformation
Review
Friday, Sept 21    Prelim 1
5   (9/24 - 10/28)       3.2
      3.3
      3.4 		Subspaces of R^n - bases, linear independence
Dimension of a subspace
Coordinates
6   (10/1 - 10/5)       4.1
      4.2
      4.3
 Introduction to linear spaces
Linear transformations and isomorphisms
The matrix of a linear transformation
7   (10/8)    Fall Break
7   (10/10 - 10/12)       5.1
      5.2 		Orthonormal bases and orthogonal projections
The Gram-Schmidt process and QR factorization
8   (10/15 - 10/19)       5.3
      5.4
      .. 		Othogonal transformations and orthogonal matrices
Least squares and data-fitting
Review
Monday, Oct 22    Prelim 2
9   (10/24 - 10/26)       6.1
      6.2 		Introduction to determinants
Properties of the determinant
10   (10/29 - 11/2)       6.3
      7.1 		Interpretations of determinants, Cramer's rule
Dynamical systems and eigenvectors
11   (11/5 - 11/9)       7.2
      7.3
      7.4 		Finding the eigenvalues of a matrix
Finding the eigenvectors of a matrix
Diagonalization
12   (11/12 - 11/16)       7.5
      7.6
      .. 		Complex eigenvalues
Stability
Review
Monday, Nov 19    Prelim 3
13   (11/21 - 11/23)    Thanksgiving Break
14   (11/26 - 11/30)       8.1
      8.2
 Symmetric matrices
Quadratic forms
15   (12/3 - 12/7)       5.5
      ..
 Inner product spaces
Review