|
Date |
|
|
Chap |
Topics |
|
Jan |
13 |
M |
1 |
Why Study ODEs? |
|
15 |
W |
1 |
ODE Review |
|
17 |
F |
2 |
Linear Systems of ODEs |
|
|
20 |
M |
|
No Class |
|
22 |
W |
2 |
Equilibrium Solutions/Direction Fields |
|
|
24 |
F |
2 |
Polar Forms/Maple-MATLAB |
|
27 |
M |
2 |
Matrices/Eigenvalue Problems |
|
29 |
W |
2 |
Fundamental Solutions |
|
31 |
F |
2 |
General Solutions/Examples |
| Feb |
3 |
M |
2 |
Nonhomogeneous Systems |
|
5 |
W |
|
Physical Applications |
|
7 |
F |
|
Exam I |
|
10 |
M |
3 |
Equilibrium Solutions |
|
12 |
W |
3 |
Bifurcations |
|
14 |
F |
3 |
Nonlinear Pendulum |
|
17 |
M |
3 |
Stability of Nonlinear Systems |
|
19 |
W |
3 |
Applications |
|
|
21 |
F |
3 |
Limit Cycles |
|
24 |
M |
3 |
Nonautonomous Systems |
|
26 |
W |
|
Chaos .... Projects |
|
28 |
F |
|
Exam II |
| |
|
|
|
Spring Break March 1-8 |
| Mar |
10 |
M |
4 |
Boundary Value Problems |
|
12 |
W |
4 |
Applications/Heat Equation |
|
14 |
F |
4 |
Linear Algebra Connections |
|
17 |
M |
4 |
Eigenfunction Expansions |
|
19 |
W |
5 |
Fourier Series I |
|
21 |
F |
5 |
Fourier Series II |
|
24 |
M |
5 |
Convergence Applications |
| |
26 |
W |
5 |
Sine-Cosine Series |
|
28 |
F |
|
Exam III |
|
|
31 |
M |
6 |
Sturm-Liouville Theory |
|
Apr |
2 |
W |
6 |
Properties - Sturm-Liouville BVPs |
|
3 |
F |
6 |
Eigenfunction Expansions |
|
7 |
M |
6 |
Fredholm Alternative |
|
9 |
W |
7 |
Classical Orthogonal Polynomials Special Functions |
|
11 |
F |
7 |
Legendre Polynomials |
|
14 |
M |
7 |
Legendre Polynomials II Bessel Functions |
|
16 |
W |
7 |
Bessel Functions I Hypergeometric Functions |
| |
17 |
R |
|
No Class |
| |
18 |
F |
|
No Class |
|
21 |
M |
7 |
Bessel Functions II More on Series Solutions |
|
23 |
W |
8 |
Variation of Parameters |
| |
25 |
F |
8 |
Green's Functions |
|
|
28 |
M |
8 |
Dirac Delta Function |
|
|
30 |
W |
8 |
Properties of Green's Functions |
|
|
|
8 |
Series Representations |
| May |
7 |
W |
|
Final Exam 8:00 AM |
|
|
|
|
Other Topics
- Numerical Solutions
- Hypergeometric equation
- Laplace transforms
- Perturbation Theory
- Divergent Series
- Historical references
- Fractional
|