Math 2130 Spring 2013
Tentative Schedule (what didn't happen)




Class 1: A bit about the field of complex numbers and other unfamiliar fields.
Class 2: A quick "review" of linear algebra
Class 3: More "review"
Class 4: Direct Sums
Class 5: Quotients
Class 6: Dual Spaces
Class 7: Tensors (part I)
Class 8: Tensors (part II)
Class 9: Exterior Algebras
Class 10: Review of Eigen-stuff
Class 11: Jordan Form (part I)
Class 12: Jordan Form (part II)
Class 13: The Matrix Exponential and Functions of Matrices
Class 14: Midterm #1
Class 15: Differential Equations
Class 16: Operator Methods: Homogeneous Equations (part I)
Class 17: Operator Methods: Homogeneous Equations (part II)
Class 18: Operator Methods: Undetermined Coefficients
Class 19: Variation of Parameters
Class 20: Matrix Methods
Class 21: Variation of Parameters Again
Class 22: Midterm #2
Class 23: Symmetry Methods
Class 24: Symmetry Methods
Class 25: Differential Galois Theory
Class 26: Differential Galois Theory
Class 27: Why You Can't Integrate That
Class 28: Free for All
Class 29: Presentations





Math 2130 Spring 2013
Schedule (what did happen)




Class 1: A bit about the field of complex numbers and other unfamiliar fields.
Class 2: more about fields (including characteristic of a ring and finite fields)
Class 3: linear independence, spanning, bases
Class 4: existence of bases and bases have the same cardinality
Class 5: row reduction, RREF, linear correspondence between columns, coordinates
Class 6: direct sums and finding bases for kernels, ranges etc.
Class 7: homework questions, equivalence relations, and quotient spaces
Class 8: rank+nullity=dimension of domain, 1st isomorphism theorem, and defining Hom/End/dual spaces
Class 9: Coordinate matrices for linear transformations and dual bases.
Class 10: More about duals and a bit about tensor products.
Class 11: Tensor non-sense, tensor algebras, symmetric algebras, and exterior algebras.
Class 12: Exterior algebras, determinants, and the cross product. Also, a bit of eigen-stuff.
Class 13: Eigen-stuff, Cayley-Hamilton Theorem
Class 14: Jordan form
Class 15: More Jordan form (explicit examples)
Class 16: matrix exponential/functions of matrices
Class 17: Introduction to Differential Equations: Definitions, Theory, Separable, Exact
Class 18: Matrix Exponential Examples. [1/3 Class on Washington trip]
Class 19: SNOW DAY. No class.
Class 20: Reduction to systems, First order linear, Operator Methods (homogeneous eqns)
Class 21: Homogeneous equations: General, constant coeff, and Cauchy-Euler
Class 22: Test returned, linear algebra stuff
Class 23: Non-homogeneous: undetermined coeff. for constant coeff and Cauchy-Euler
Class 24: Non-homogeneous: variation of parameters, Wronskians
Class 25: Cramer's rule (proof), Abel's theorem, more variation of params.
Class 26: Linear systems of ODEs: matrix techniques - homogeneous and var. of params.
Class 27: Linear systems of ODEs: examples
Class 28: Test #2 (in class)
Class 29: Last things - a bit of differential Galois theory & symmetry methods




Notes: Too much abstract stuff at the beginning. Would have been better to see 
       some DEs closer to the start of the course to keep those frustrated with 
       proofs from becoming discouraged. Tests were delayed too long. Those without
       a background in DEs needed longer to absorb the basics.


January

Sunday
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday


1
2
3
4
5


6
7
8
9
10
11
12


13
14
Class 1
16
Class 2
18
19


20
21
Class 3
23
Class 4
25
26


27
28
Class 5
30
Class 6





February

Sunday
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday


1
2


3
4
Class 7
6
Class 8
8
9


10
11
Class 9
13
Class 10
15
16


17
18
Class 11
20
Class 12
22
23


24
25
Class 13
27
Class 14





March

Sunday
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday


1
2


3
4
Class 15
6
Class 16
8
9


10
No Class
No Class
No Class
No Class
15
16


17
18
Class 17
20
Class 18
22
23


24
25
Class 19
27
Class 20
29
30


31





April

Sunday
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday


1
No Class
3
Class 21
5
6


7
8
Class 22
10
Class 23
12
13


14
15
Class 24
17
Class 25
19
20


21
22
Class 26
24
Class 27
26
27


28
29
Class 28





May

Sunday
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday


1
Class 29
3
4


5
6
7
Presentations
9am-11:30am
9
10
11


12
13
14
15
16
17
18


19
20
21
22
23
24
25


26
27
28
29
30
31








Last Updated: August 5th, 2013