Suggested Lecture Schedule
1
The
Geometry
of
the
Plane
and
3-space 11 Lectures
1.1
Vectors
and
Arrows . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Length
and
Direction . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3
L1Des,
Planes
and
the
Cross Product . . . . . . . . . . . . . . . . . 4
1.4 Projections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.5
L1Dear
Dependence
and
Independence . . . . . . . . . . . . . . . 1
2 Matrices
llDd
Linear Equations
18
Lectures
2.1 The Algebra
of
Matrices . . . . . . . . . . . . . . . . . . . . . . . . 2
~
2.2 Application: Generating Codes with Matrices . . . . . . . . . . . 1
2.3 Inverse
and
Transpose . . . . . . . . . . . . . . . . . . . . . . . . . 2
~
2.4 Systems
of
Linear Equations . . . . . . . . . . . . . . . . . . . . . . 2
2.5 Application: Electric Circuits . . . . . . . . . . . . . . . . . . . . . 1
2.6 Homogeneous Systems; Linear Independence . . . . . . . . . . . 2
2.7 Elementary Matrices
and
LU
Factorization . . . . . . . . . . . . . 3
2.8
I.DU
Faclori.zalion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2.9 More
on
the
Inverse
of
a Matrix. . . . . . . . . . . . . . . . . . . . 2
3 Determinants, Eigenvalues, Eigenvectors 11 Lectures
3.1
The Determinant
of
a Matrix . . . . . . . . . . . . . . . . . . . . . 2
3.2 Properties of Determinants . . . . . . . . . . . . . . . . . . . . . . 3
3.3 Application: Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . l
3.4 Eigenvalues
and
Eigenvectors . . . . . . . . . . . . . . . . . . . . . l
~
3.5 Similarity
and
Diagonalization . . . . . . . . . . . . . . . . . . . . l
~
3.6 Application: Linear Recurrence Relations . . . . . . . . . . . . . . 1
3.7 Application: Markov Chains . . . . . . . . . . . . . . . . . . . . . . 1
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