__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. |