## Math 475: Differential equations

## Fall 2017

Class Time | M,W 9:00am – 10:15am |

Class Location | Tempe – WGHL202 |

Instructor | Sébastien Motsch |

Office | WXLRA 836 |

smotsch@asu[dot]edu | |

Office Hours | M,W 1:00pm – 3:00pm |

Class webpage | www.seb-motsch.com/teaching |

## Textbook

- M. Hirsch, S. Smale and R. Devaney,
*Differential Equations, Dynamical Systems, and an Introduction to Chaos*(2012)

### Course description

- Linear systems of ODE
*(Chap.1-6)* - Non-linear dynamical systems
*(Chap.7-9)* - Limit sets
*(Chap.10)*

A **syllabus** is also available here.

The first Mid-term is scheduled on *Monday September 25th* and the second for Monday November 6th (confirmed) in class. The *Wednesday December 6th* at 7:30am in the usual classroom.

### Class Schedule

Aug 21 – 23 | 1st order ODE (chap.1), Planar linear systems (chap.2) |

Aug 28 – 30 | Planar linear systems (chap.3) |

Sep 4 – 6 | Labor day – Planar linear systems (chap.3-4) |

Sep 11 – 13 | Classification, Higher dimension (chap.4-5) |

Sep 18 – 20 | Higher dimension (chap.5-6), practice midterm (solution) |

Sep 25 – 27 | Midterm 1 (solution), Exp. matrix (chap.6) |

Oct 2 – 4 | Non-linear systems (chap.7) |

Oct 9 – 11 | Fall Break |

Oct 16 – 18 | Non-linear systems, linearization (chap.7-8) |

Oct 23 – 25 | Phase transitions, Isoclines (chap.8-9) |

Oct 30 – Nov 1 | Isoclines (chap.9), review midterm (solution) |

Nov 6 – 8 | Midterm 2 (solution) |

Nov 13 – 15 | Lyapunov, Gradient-Hamiltonian systems (chap.9) |

Nov 20 – 22 | Limit behavior(chap.10) |

Nov 27 – 29 | Review final, practice final (solution) |

### Class homework

Aug 28 | Chap.1: 2, 7, 8, 9, 11, 12 (solution HW1) |

Sep 6 | Chap.2: 2, 3, 6, 10, Chap.3: 2(i,iii,v), 3 (solution HW2) |

Sep 13 | Chap.3: 4, 6, 10, 11, Chap.4: 2, 3, 5 (solution HW3) |

Sep 20 | Chap.5: 2, 3, 5a-f, 11, Chap.6: 1a-f (solution HW4) |

Oct 4 | Chap.6: 3, 5a, 6a, 12, 13 (solution HW5) |

Oct 16 | Chap.7: 1, 2, 3, 4, 6 (solution HW6) |

Oct 23 | Chap.8: 1, 2, 5, 6, 7, 12 (solution HW7) |

Oct 30 | Chap.8: 4, 8, 9, Chap.9: 1 (solution HW8) |

Nov 20 | Chap.9: 2, 6, 7 (solution HW9) |

Nov 27 | Chap.9: 8a-d, Chap.10: 1,2,4,7 (solution HW10) |

### Extra

- Visualization of phase portraits