**Instructor:** Patrick Lutz

**Email:** Reverse of ude.yelekreb “at” ztulgp

**Office:** 840 Evans

**Office Hours:** MWF 9-10, TuTh 3-4

**Final Week Office Hours:** M 9-10, WF 9-11, TuTh 12-1 and 3-4

Date | Topics | Readings | Homework Problems | Quiz | Worksheet | |
---|---|---|---|---|---|---|

1 | 6/19 | Intro, review of complex numbers | Handout, Appendix B (complex numbers) | HW 1 | No quiz today | No worksheet today |

2 | 6/20 | Linear Equations and Gaussian Elimination | 1.1, 1.2 | 1.1: 3, 11, 15, 23, 24 1.2: 5, 7, 11, 15, 16, 17, 18, 23, 26, 30 |
Quiz, Solutions | Worksheet |

3 | 6/21 | Vectors | 1.3 | 1.3: 1, 5, 9, 11, 14, 15, 22, 23 | Quiz, Solutions | Worksheet |

4 | 6/22 | Linear Independence, Matrices | 1.7, 1.4 | 1.7: 1, 11, 17, 21, 22, 23, 33, 36 1.4: 1, 5, 7, 9, 11, 17, 18, 24 |
Quiz, Solutions | Worksheet |

5 | 6/23 | Linear Transformations | 1.8, 1.9 | 1.8: 1, 3, 7, 9, 13, 14, 17, 22, 30, 32 1.9: 1, 5, 9, 17, 22, 25, 35 |
Quiz, Solutions | Worksheet |

6 | 6/26 | Geometry of solution sets, Review | 1.5, 1.9 | 1.5: 5, 11, 24, 26, 38, 39 Supplementary exercises: 14, 18 |
Quiz, Solutions | Worksheet |

7 | 6/27 | Matrix Algebra | 2.1 | 2.1: 1, 2, 3, 7, 10, 12, 18, 19, 22, 23 | Quiz, Solutions | Worksheet |

8 | 6/28 | Inverses | 2.2, 2.3 | 2.2: 1, 5, 9, 10, 12, 13, 16, 20, 31, 38 2.3: 1, 3, 5, 12, 13, 21, 36 |
Quiz, Solutions | Worksheet |

9 | 6/29 | Subspaces, Bases | 2.6 | 2.6: 2, 3, 5, 11, 13, 17, 18, 27, 28 | Quiz, Solutions | Worksheet |

10 | 6/30 | Bases, Dimension | 2.7, 4.2 | 2.6: 22, 23 2.7: 9, 16, 21, 23, 24 4.2: 1, 3, 5 4.3: 13, 21, 23, 25 |
Quiz, Solutions | Worksheet |

11 | 7/03 | Vector Spaces | 4.1, 4.2, 4.3 | 4.1: 1, 5, 6, 7, 8, 9, 21, 22, 25, 26, 32 | Quiz, Solutions | Worksheet |

7/04 | Fireworks |
|||||

12 | 7/05 | Coordinates | 2.7, 4.4 | 4.4: 1, 5, 13, 18, 20, 23, 24, 26, 27, 28, 31, 32 | Quiz, Solutions | Worksheet |

13 | 7/06 | More on Bases | 4.5, 5.4 | 4.2: 31, 35 4.3: 31, 32 4.5: 21, 23, 25 5.4: 2, 6, 9 |
Quiz, Solutions | Worksheet |

14 | 7/07 | Change of Basis | 4.7 | 4.5: 26, 27, 30 4.7: 3, 9, 10, 20a |
Quiz, Solutions | Worksheet |

15 | 7/10 | More Change of Basis | 4.5, 4.7 | 2.3: 28, 30 4.5: 9, 11, 13 4.7: 13, 14 |
Quiz, Solutions | Worksheet |

16 | 7/11 | Determinants | 3.1, 3.2 | 3.1: 3, 15, 22 3.2: 7, 16, 19, 29, 33 4.6: 7, 9 |
Quiz, Solutions | Worksheet |

17 | 7/12 | Eigenvalues | 5.1, 5.2 | 5.1: 10, 11, 20, 21, 24, 26, 29, 31 5.2: 1, 2, 9, 17, 19 |
Quiz, Solutions | Worksheet |

18 | 7/13 | Diagonalization | 5.3, 5.4 | 5.1: 13, 15 5.2: 3, 5 5.3: 1, 4, 5, 9, 13, 21, 22, 23, 24 |
Quiz, Solutions | Worksheet |

19 | 7/14 | More Diagonalization | 5.3, 5.4 | No homework | No quiz today | No worksheet today |

7/17 | Midterm |
|||||

20 | 7/18 | Review midterm, Complex Eigenvalues | 5.5 | 5.5: 1, 2, 3, 4, 5, 6 Supplementary Exercises: 2, 3, 9 |
No quiz today | Worksheet |

21 | 7/19 | Geometry of ℝ^{n} |
6.1 | 5.5: 7, 13 6.1: 1, 2, 3, 5, 7, 9, 13, 19, 28 |
Quiz, Solutions | Worksheet |

22 | 7/20 | Orthogonal Basis | 6.2 | 6.2: 7, 9, 17, 21, 23a-c, 26 | Quiz, Solutions | Worksheet |

23 | 7/21 | Projections, Gram-Schmidt | 6.3, 6.4 | 6.3: 1, 3, 4, 9, 11, 21a-d, 23, 24 6.4: 9, 11, 22 |
Quiz, Solutions | Worksheet |

24 | 7/24 | Least Squares | 6.5 | 6.2: 24, 28 6.3: 22 6.5: 1, 3, 7, 13, 17, 18a-c, 20 |
Quiz, Solutions | Worksheet |

25 | 7/25 | Inner product spaces | 6.7 | 6.7: 1, 3, 5, 7, 14, 21, 23, 25, 26 | Quiz, Solutions | Worksheet |

26 | 7/26 | Symmetric matrices | 7.1, 7.2 | 7.1: 1, 17, 26, 27, 29 | Quiz, Solutions | Worksheet |

27 | 7/27 | Intro to ODEs | 4.2, 6.2 | 4.2: 3, 5, 10, 13, 15, 26 6.2: 1, 19 |
No quiz today | Worksheet |

28 | 7/28 | Repeated and Complex roots | 4.2, 4.3 | 4.2: 19, 37 4.3: 3, 13, 21, 22, 28, 36 6.2: 5, 9, 17 |
Quiz, Solutions | Worksheet |

29 | 7/31 | Inhomogeneous ODEs | 4.4, 4.5 | 4.4: 11, 12, 13, 21, 29 4.5: 2, 5, 17, 29 |
Quiz, Solutions | Worksheet |

30 | 8/01 | Systems of ODEs | 6.1, 9.1, 9.4 | 6.1: 7, 9 9.1: 3, 7, 11 9.4: 5, 26, 28 Optional: 6.1 34, 35 |
Quiz, Solutions | Worksheet |

31 | 8/02 | More on Systems of ODEs | 9.4, 9.5 | 9.4: 37 9.5: 11, 14, 17, 26, 31, 35 |
Quiz, Solutions | Worksheet |

32 | 8/03 | Complex eigenvalues and pictures | 9.5, 9.6 Optional (but cool): 9.8 |
9.5: 41, 49 9.6: 1, 3, 4, 23 Optional: 9.8 26, 27 |
Quiz, Solutions | Worksheet |

33 | 8/04 | Intro to PDEs | 10.1, 10.2, Notes | HW 32 | Quiz, Solutions | Worksheet |

34 | 8/07 | Fourier Series | 10.3, 10.4 (and Lay 6.8) | NS&S 10.3: 9, 12, 14, 16 Lay 6.8: 13 |
Quiz, Solutions | Worksheet |

35 | 8/08 | Fourier Series and the Heat Equation | 10.4, 10.5 | Optional: 10.4: 5, 7, 8, 10, 17, 19 | Quiz, Solutions | Worksheet |

36 | 8/09 | Other PDEs | 10.6 | No homework | No quiz today | No worksheet today |

37 | 8/10 | Review | Everything | No homework | No quiz today | No worksheet today |

8/11 | Final |

10% quizzes, 10% HW, 30% midterm, 50% final.

Every day at the beginning of class there will be a 10 minute, 4 point quiz on the previous day’s material. It is my intention that if you understood the previous day’s material then the quiz should not be tricky and should take less than 10 minutes. The lowest 7 scores will be dropped. There are no make-up quizzes.

Homework is assigned daily (and you should do it daily) and it is due Tuesdays and Fridays at the beginning of class. One problem per day will be graded for accuracy. The lowest 2 scores will be dropped.

When answering homework questions in this class, you are required to show your work or give an explanation of your answer. You don’t have to write a lot, but you should write enough so that any of your classmates would be convinced that your answer is correct after reading your explanation. If you fail to do this, you will not receive full credit.

There will be a midterm on Monday, July 17 in class and a final on Friday, August 11 in class. Both will be 2 hours long and closed book. Your final score will replace your score in each other category (midterm, HW, and quizzes) if it helps.

- The Matrix Cookbook: Useful collection of facts and algorithms in linear algebra. It includes many things we did not learn about, but it is a good resource to be aware of if you encounter linear algebra in the future.
- Math 54 worksheets
- Cool visualization of solutions to the heat equation (made by Kyle Miller) and Visualization of solutions to the wave equation (also by Kyle Miller)
- David Nadler’s Math 54 page. Lectures 19-22 in particular are similar to the way I presented the material in class and may be useful to you.
- Vivek Shende’s Math 54 page. The lectures on PDEs in particular are similar to the way I presented the material in class and may be useful to you.
- Tool (made by Kyle Miller) for visualizing linear transformations
- Demo of word2vec (scroll to the section labelled “Bonus App”)
- Piazza
- Student Learning Center drop-in tutoring
- Archive of past exams
- Even more past exams