**Lecture** | **Topic** | **File** | **Code** | ** Textbook Sections ** |

1-2 | Neurons and Synapses | [ ppt ] | | #1.1 |

2 | Physics Review | [ pdf ] | | |

3-4 | Equation of passive membrane | [ pdf ] | | #2.1.2-#2.1.4 |

4 | Derivation of Nernst potential | [ pdf ] | | #2.1.1 |

5 | Time-dependent current; stability analysis | [ pdf ] | | #3.2 |

6 | Introduction to Matlab: sample programs | | [ myExp.m ] [ plots.m ] | |

7 | Numerical solution to ODEs: Euler Method | [ pdf ] |
[ myEuler.m ] [ myEulerScript.m ] | |

8 | Integrate-and-Fire Models | | [ IandF.m ] [ IandFquadratic.m ] | #3.3.8, #8.1.1, #8.1.3 |

9 | 1D Bifurcations: saddle-node & transcritical | | | #3.3.3-#3.3.7 |

10-12 | 2D Vector Fields and Linear Systems | [ pdf ] |
[ PhasePlane2D.m ] | #4.1.1-#4.2.5 |

13-14 | FitzHugh-Nagumo Model; Hopf Bifurcation | | [ FN_Hopf.m ] | #4.2.6, #4.3.5, #6.1.3-#6.1.4 |

15 | Morris-Lecar Model | [ T&E ]
| [ ML_Hopf.m ] [ ML_SHOB.m ] | #5.1.2; Terman & Ermentrout |

16-17 | Hodgkin-Huxley Model | [ pdf ] | [ HH.m ] | #2.3 |

18 | 2D reduction of Hodgkin-Huxley Model | | [ HH_2D.m ] | #5.2.1 |

19-20 | Bifurcations from Rest to Spiking | [ pdf ] |
[ ML_Hopf.m ] [ ML_SHOB.m ] | #1.2, #4.3, #6.1-6.2, #7.1-#7.2 |

21-22 | Models of Bursting | [ T&E ] | [ Square-Wave ] [ Elliptic ] | #9.1-#9.3; Terman & Ermentrout |

23-24 | Propagation of Action Potential | [ pdf ] | | #2.3.3-#2.3.4 |

25 | Synaptically coupled cells and the PRC | | | |