Penn State University Department of Mathematics Eberly College of Science
Syllabus


Wk Lec Date Topic Book Hwk
1


2


3


4


5


6


7


8


9


10


11


12


13


14


15


1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
01/12
01/14
01/16
01/19
01/21
01/23
01/26
01/28
01/30
02/02
02/04
02/06
02/09
02/11
02/13
02/16
02/18
02/20
02/23
02/25
02/27
03/01
03/03
03/05
03/15
03/17
03/19
03/22
03/24
03/26
03/29
03/31
04/02
04/05
04/07
04/09
04/12
04/14
04/16
04/19
04/21
04/23
04/26
04/28
04/30
Systems of Linear Equations
Gauss-Jordan Elimination
Gauss-Jordan Elimination in Matrix Notation
Introduction to Solutions of Linear Systems
Introduction to Linear Transformations and Their Inverses
Linear Transformations in Geometry
The Inverse of a Linear Transformation
Matrix Products
Image and Kernel of a Linear Transformation
Subspaces. Bases and Linear Independence
The Dimension of a Subspace
Snowstorm. No class
Coordinates
Introduction to Linear Spaces
Linear Transormations
Coordinates in a Linear Space
Orthonormal Bases and Orthogonal Projections
Gram-Schmidt Process and QR Factorization
Orthogonal Transformations and Orthogonal Matrices
Least Squares and Data Fitting
Inner Product Spaces
Review
Review
Midterm
Introduction to Determinants
Properties of the Determinant
Geometrical Interpretations of the Determinant
Eigenvalues and Eigenvectors
Characteristic Polynomial
Dynamical Systems
Eigenbasis and Eigenspace; Multiplicity of eigenvalues
Complex eigenvalues
Diagonalizability
The Jordan Canonical Form
Stability
Continuous Dynamical Systems
Complex case
Linear Differential Equations
Symmetric Matrices
Symmetric Matrices
Quadratic Forms
Singular Values
Review of Linearity
Review of Orthogonality
Review of the Eigenvalue Problem
1.1
1.2
1.3
1.3
2.1
2.2
2.3
2.4
3.1
3.2
3.3

3.4
4.1
4.2
4.3
5.1
5.2
5.3
5.4
5.5



6.1
6.2
6.3
7.2
7.2
7.1
7.3
7.5
7.4
Notes
7.6
9.1
9.2
9.3
8.1
8.1
8.2
8.3







#1


#2


#3


#4


#5


#6





#7


#8


#9


#10


#11


#12


#13