# Lecture plan

This plan is tentative and can (and probably will) be changed during the semester. The references can all be found in the textbook.

Week | Subjects | References |
---|---|---|

02 | The algebra of complex numbers. Point representations. Polar forms | Saff-Snider 1.1-1.3 |

03 | The complex exponential. Powers and roots | Saff-Snider 1.4-1.5 |

04 | Second-order linear equations. Homogeneous equations with constant coefficients. Harmonic motion | Polking 4.1, 4.3-4.5 |

05 | Inhomogeneous equations. Undetermined coefficients. Variation of parameters. Forced harmonic motion | Polking 4.6-4.7 |

06 | Systems of linear equation. Row reduction and echelon forms. Vectors. The Matrix equation Ax=b | Lay 1.1-1.4 |

07 | Solution sets of linear systems. Applications of linear systems. Linear Independence | Lay 1.5-1.7 |

08 | Linear transformations. Matrices of linear transformations. Linear models | Lay 1.8-1.10 |

09 | Matrix operations. Inverse matrices. Determinants. LU factorization | Lay 2.1-2.3, 2.5, 3.1-3.2 |

10 | Vector spaces and subspaces. Null spaces, column spaces and linear transformations. Linear independents sets and bases | Lay 4.1-4.3 |

11 | Coordinate systems. Dimensions and ranks. Applications to Markov chains | Lay 4.4-4.6, 4.9 |

13/14 | Eigenvectors and eigenvalues. The characteristic equation. Diagonalization. Complex eigenvalues | Lay 5.1-5.3, 5.5 |

14/15 | Systems of linear differential equations. Inner product, length and orthogonality | Polking 4.2, Lay 5.7, 6.1-6.2 |

15/16 | Orthogonal projections. The Gram-Schmidt process. Least-square problems. Applications to linear models | Lay 6.3-6.6 |

16/17 | Diagonalization of symmetric matrices. Quadratic forms. Exam practice | Lay 7.1-7.2 |