# Department of Mathematics Syllabus

This syllabus is advisory only. For details on a particular instructor's syllabus (including books), consult the instructor's course page. For a list of what courses are being taught each quarter, refer to the Courses page.

## MAT 119A: Ordinary Differential Equations

**Approved:**2003-01-01, A. Schwarz

**Suggested Textbook:**(actual textbook varies by instructor; check your instructor)

Search by ISBN on Amazon: 0738204536

**Suggested Schedule:**

Lecture(s) |
Sections |
Comments/Topics |

1-3 |
1-d systems |
Phase space analysis, fixed points & stability, existence & uniqueness flow on the circle |

4-6 |
1-d bifurcation theory |
Saddle-node bifurcation, transcritical bifurcation, pitchfork bifurcation, catastrophes |

7-9 |
Linear systems with constant coeffients |
Canonical form & classification, stability |

10-17 |
2-d systems |
Phase place analysis: fixed points, nullclines & limit set; existence & uniqueness; stability: linearization & Lyapunov function; special systems: conservative, gradient & reversible systems; index theory; coupled oscillators & quasiperiodic orbits; poincare map: stability of periodic orbit; iterative methods for solving equations |

18-25 |
Limit cycles |
Poincare-Bendixson theorem, lienard systems, weakly nonlinear oscillators, relaxation oscillators |

26-29 |
2-d Bifurcation Theory |
Saddle-node, transcritical and pitchfork bifurcations; hopf bifurcation; homoclinic bifurcation |