September

4:

§1.1

Introductory Remarks: What is the linear algebra?

6:

§1.2

Systems of linear equations and Row Reduction

9:

§1.3, 1.4

Vector equations; Matrix-vector product

11:

§1.5, 1.6

Solution sets of linear systems; Applications

13:

§1.7

Linear Independence

16:

§1.8

Linear transformations - Geometry

18:

§1.9

Linear transformations - Matrices

20:

§1.10

Applications

23:

§2.1, 2.2

Matrix multiplication and matrix inversion

25:

§2.3

Invertible matrices

27:

§2.4

Partitioned matrices

30:

§2.5

LU-factorization of matrices

October

2:

§2.6, 2.7

Applications to economics and to computer graphics

4:

§2.8

Column space and null space of a matrix

7:

§2.9

Dimension and Rank

9:

Review

11:

First Hour Exam

14:

Holiday

15:

§3.1

Introduction to determinants

16:

§3.2, 3.3

Properties of determinants — Cramer’s Rule

18:

§3.3

Geometry of determinants

21:

§4.1

Vector spaces and subspaces

23:

§4.2

The image and kernel of a linear transformation

25:

§4.3

Linearly independent sets; Bases

28:

§4.4

Coordinate systems

30:

§4.5, 4.6

Dimension of a subspace; Rank of a matrix

November

1:

§4.7

Change of basis

November

4:

§4.8

Difference equations

6:

§4.9

Stochastic matrices and Markov chains

8:

Review

11:

Second hour exam

13:

§5.1

Introduction to eigenvalues and eigenvectors

15:

§5.2

Eigenvalues and the characteristic polynomial

18:

§5.3, 5.4

Diagonalization, eigenvectors of linear transformations

20:

§5.5

Complex eigenvalues

22:

§5.6

Discrete dynamical systems

25:

§5.7

Continuous dynamical systems — differential equations

27:

Fall Recess

29:

Fall Recess

December

2:

§6.1, 6.2

Inner product, orthogonality

4:

§6.3, 6.4

Orthogonal projection, Gram-Schmidt

6:

§6.5

Least-squares problems

9:

Review

11:

Review