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Syllabus

Class | Date | Day | Title | Sections | Announcements |
---|---|---|---|---|---|

Lecture 01 | 9/08 | W | The Geometry of Linear Equations. | 1.1-2.1 | |

Lecture 02 | 9/10 | F | Elimination with Matrices. | 2.2-2.3 | |

Lecture 03 | 9/13 | M | Matrix Operations and Inverses. | 2.4-2.5 | |

Lecture 04 | 9/15 | W | A = LU and A = LDU Factorization. | 2.6 | Problem Set 1 Due 9/16 |

Lecture 05 | 9/17 | F | Permutations, Dot Products, and Transposes. | 2.7 | |

Lecture 06 | 9/20 | M | Vector Spaces and Subspaces. | 3.1 | |

Lecture 07 | 9/22 | W | The Nullspace: Solving Ax=0. | 3.2 | Problem Set 2 Due 9/23. |

Lecture 08 | 9/24 | F | Solving $Ax=b$ for nonsquare $A$, Row-reduced Echelon Form. | 3.3-3.4 | |

Lecture 09 | 9/27 | M | Independence, Dimension, and Bases. | 3.5 | |

Lecture 10 | 9/29 | W | The Four Fundamental Subspaces. | 3.6 | Problem Set 3 Due 9/30. |

Lecture 11 | 10/01 | F | EXAM REVIEW. | 3.6 | |

Exam 1 | 10/04 | M | EXAM: Chapters 1 to 3.5 | ||

Lecture 12 | 10/06 | W | Graphs and Networks. | 8.2 | Problem Set 4 Due 10/07. |

Lecture 13 | 10/08 | F | Orthogonality and Subspaces | 4.1 | |

10/11 | M | COLUMBUS DAY | |||

Lecture 14 | 10/13 | W | Projections. | 4.2 | Problem Set 5 Due 10/14 |

Lecture 15 | 10/15 | F | Least Squares Approximations. | 4.3 | |

Lecture 16 | 10/18 | M | Orthonormal Bases, Gram-Schmidt, and $A=QR$. | 4.4 | |

Lecture 17 | 10/20 | W | Fourier Series and Orthogonal Polynomials. | 8.5 | Problem Set 6 Due 10/21 |

Lecture 18 | 10/22 | F | Properties of Determinants. | 5.1 | |

Lecture 19 | 10/25 | M | Formulas for Determinants; Jacobians. | 5.2-5.3 | |

Lecture 20 | 10/27 | W | Eigenvalues and Eigenvectors. | 6.1 | Problem Set 7 Due 10/28 |

Lecture 21 | 10/29 | F | Similar Matrices, Diagonalization, and Powers of $A$ | 6.6, 6.2 | |

Lecture 22 | 11/01 | M | EXAM REVIEW | ||

Exam 2 | 11/03 | W | EXAM: Chapter 1 to 5.3 and 8.2,8.5 | ||

Lecture 23 | 11/05 | F | Markov Matrices | 8.3 | |

Lecture 24 | 11/08 | M | Differential Equations | 6.3 | |

Lecture 25 | 11/10 | W | Symmetric Matrices. | 6.4 | Problem Set 8 Due 11/11 |

Lecture 26 | 11/12 | F | Positive Definite Matrices. | 6.5 | |

Lecture 27 | 11/15 | M | Defective Matrices: Jordan Forms and Generalized Eigenvectors. | 6.6 | |

Lecture 28 | 11/17 | W | Singular Value Decompositions. | 6.7 | Problem Set 9 Due 11/18. |

Lecture 29 | 11/19 | F | Matrices in Engineering. | 8.1 | |

Lecture 30 | 11/22 | M | Linear Operators on Functions. | ||

Lecture 31 | 11/24 | W | Sparse Matrices and Iterative Methods. | 9.3 | Problem Set 10 Due 11/29. |

11/26 | F | THANKSGIVING. | |||

Lecture 32 | 11/29 | M | EXAM REVIEW. | ||

Exam 3 | 12/01 | W | EXAM: Chapters 1 to 6.7 and 8.1, 8.3, 8.5. | ||

Lecture 33 | 12/03 | F | Numerical Linear Algebra | 9.1-9.2 | |

Lecture 34 | 12/06 | M | Complex Matrices and FFTs | 10.1-10.3 | |

Lecture 35 | 12/08 | W | Course Review. | ||

Final Exam | TBD |