Week |
Topics |
1/17-1/19 |
ODEs and PDEs. Exponential ODE. |
1/22-1/26 |
Complex Exponentials |
1/29-2/2 |
Matrix Exponentials |
2/5-2/9 |
Second-order linear ODEs. Oscillators |
2/12-2/16 |
Midterm I. Forced oscillators and
resonance. |
2/19-2/23 |
Laplace transform. Delta functions.
Boundary value problems |
2/26-3/2 |
Linear algebra. Gauss method. Determinants. |
3/5-3/9 |
Eigenvalues. Diagonalization. |
3/12-3/16 |
Linear Maps. Abstract vector spaces. |
3/19-3/23 |
Midterm II. Solving linear systems
by eigenvalue method. |
3/26-3/30 |
Spring Break. |
4/2-4/6 |
Computing matrix exp. Linear flows.
Variation of parameters. |
4/9-4/13 |
Nonlinear ODEs. Existence and uniqueness. |
4/16-4/20 |
Phase portraits. Equilibria and stability. |
4/23-4/27 |
Periodic orbits. 2D Hamiltonian ODEs.
Numerics. |
4/30-5/4 |
Forced pendulum. Lorentz equation. |