# 12-267/Navigation

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# | Week of... | Notes and Links |
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1 | Sep 10 | About This Class. Monday: Introduction and the Brachistochrone. Tuesday: More on the Brachistochrone, administrative issues. Tuesday Notes. Friday: Some basic techniques: first order linear equations. |

2 | Sep 17 | Monday: Separated equations, escape velocities. HW1. Tuesday: Escape velocities, changing source and target coordinates, homogeneous equations. Friday: Reverse engineering separated and exact equations. |

3 | Sep 24 | Monday: Solving exact equations, integration factors. HW2. Tuesday: Statement of the Fundamental Theorem. Class Photo. Friday: Proof of the Fundamental Theorem. |

4 | Oct 1 | Monday: Last notes on the fundamental theorem. HW3. Tuesday Hour 1: The chain law, examples of variational problems. Tuesday Hour 2: Deriving Euler-Lagrange. Friday: Reductions of Euler-Lagrange. |

5 | Oct 8 | Monday is thanksgiving. Tuesday: Lagrange multiplyers and the isoperimetric inequality. HW4. Friday: More Lagrange multipliers, numerical methods. |

6 | Oct 15 | Monday: Euler and improved Euler. Tuesday: Evaluating the local error, Runge-Kutta, and a comparison of methods. Friday: Numerical integration, high order constant coefficient homogeneous linear ODEs. |

7 | Oct 22 | Monday: Multiple roots, reduction of order, undetermined coefficients. Tuesday: From systems to matrix exponentiation. HW5. Term Test on Friday. |

8 | Oct 29 | Monday: The basic properties of matrix exponentiation. Tuesday: Matrix exponentiation: examples. Friday: Phase Portraits. HW6. Nov 4 was the last day to drop this class |

9 | Nov 5 | Monday: Non-homogeneous systems. Tuesday: The Catalan numbers, power series, and ODEs. Friday: Global existence for linear ODEs, the Wronskian. |

10 | Nov 12 | Monday-Tuesday is UofT November break. HW7. Friday: Series solutions for . |

11 | Nov 19 | Monday: is irrational, more on the radius of convergence. Tuesday (class): Airy's equation, Fuchs' theorem. Tuesday (tutorial): Regular singular points. HW8. Friday: Discussion of regular singular points.. |

12 | Nov 26 | Monday: Frobenius series by computer. Qualitative Analysis Handout (PDF). Tuesday: The basic oscillation theorem. Handout on the Frobenius Method. HW9. Friday: Non-oscillation, Sturm comparison. |

13 | Dec 3 | Monday: More Sturm comparisons, changing the independent variable. Tuesday: Amplitudes of oscillations. Last class was on Tuesday! |

F1 | Dec 10 | |

F2 | Dec 17 | The Final Exam (time, place, style, office hours times) |

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