**Linear Algebra II & Tutorial 2b **

(G30 Program, Nagoya University, Spring 2020)

To be prepared for the course you should recall the content of Linear Algebra I.

As in Linear Algebra I, there will be just one grade for both the lecture Linear Algebra II and the Math. Tutorial 2b. It will be mostly based on the points achieved in the homework. If possible, I might include Quizzes in some way.

If an exam is possible (not decided yet by the university), there will be one at the end of the semester. The percentage for each part will be decided later. (Just try your best at the homework!)

The following gives a tentative overview of the topics we will cover each week.

Week 01 (04/20-04/26): Vector spaces (Notes: Lecture 1, Videos: Lecture 1-1 , Lecture 1-2, Homework: HW1)

Week 02 (04/27-05/01): Linear maps (Notes: Lecture 2, Video: Lecture 2, Homework: HW2)

Golden week

Week 03 (05/11-05/17): The matrix of a linear map (Notes: Lecture 3, Video: Lecture 3, Homework: HW3)

Week 04 (05/18-05/24): Determinants & Mathematical induction (Notes: Lecture 4, Video: Lecture 4, Homework: HW4)

Week 05 (05/25-05/31): Properties of the determinant I (Notes: Lecture 5, Video: Lecture 5, Homework: HW5)

Week 06 (06/01-06/07): Properties of the determinant II (Notes: Lecture 6, Video: Lecture 6, Homework: Recall Week 1-6)

Week 07 (06/08-06/14): Eigenvalues and eigenvectors I (Notes: Lecture 7, Video: Lecture 7, Homework: HW6)

Week 08 (06/15-06/21): Eigenvalues and eigenvectors II (Notes: Lecture 8, Video: Lecture 8, Homework: HW7)

Week 09 (06/22-06/28): Eigenvalues and eigenvectors III (Notes: Lecture 9, Video: Lecture 9, Homework: HW8)

Week 10 (06/29-07/05): Applications (Notes: Lecture 10, Video: Lecture 10, Homework: Play around in python)

Week 11 (07/06-07/12): Continuous dynamical systems (Notes: Lecture 11, Video: Lecture 11, Homework: Recall Week 7-10)

Week 12 (07/13-07/19): Linear differential equations I (Notes: Lecture 12, Video: Lecture 12, Homework: HW9)

Week 13 (07/20-07/26): Linear differential equations II (Notes: Lecture 13, Video: Lecture 13, Homework: Prepare for the exam)

Week 14 (07/27-08/02): Review (Review exercises, Video: Lecture 14)

The tutorial will be done via Zoom meetings each week. The meetings will be every Thursday at 14:45 and meeting IDs are posted in the Facebook group and at the NUCT course.

**Materials**- Lecture overview (ver. 13, 21th July)
- Lecture notes: Lecture 1, Lecture 2, Lecture 3, Lecture 4, Lecture 5, Lecture 6, Lecture 7, Lecture 8, Lecture 9, Lecture 10, Lecture 11, Lecture 12, Lecture 13
- Lecture video: Lecture 1-1 , Lecture 1-2, Lecture 2, Lecture 3, Lecture 4, Lecture 5, Lecture 6, Lecture 7, Lecture 8, Lecture 9, Lecture 10, Lecture 11, Lecture 12, Lecture 13, Lecture 14 (Review)
- Homework: HW1 (Sol), HW2 (Sol), HW3 (Sol), HW4 (Sol), HW5 (Sol), HW6 (Sol), HW7 (Sol), HW8 (Sol), HW9 (Sol)
- Tutorial notes: Tutorial 1, Tutorial 2, Tutorial 3, Tutorial 4, Tutorial 5, Tutorial 6, Tutorial 7 (Quiz), Tutorial 8, Tutorial 9, Tutorial 10, Tutorial 11, Tutorial 12, Tutorial 13, Tutorial 14, Tutorial 15 (Review)
- Review exercises (Solution - Try by yourself first!)
- Final exam: Final exam (Solution)

**Grading & Homework submission****:**As in Linear Algebra I, there will be just one grade for both the lecture Linear Algebra II and the Math. Tutorial 2b. It will be mostly based on the points achieved in the homework. If possible, I might include Quizzes in some way.

If an exam is possible (not decided yet by the university), there will be one at the end of the semester. The percentage for each part will be decided later. (Just try your best at the homework!)

- Please submit your homework at NUCT as one pdf file in the Assignment menu.

Here is an explanation of how to do so: How use Assignments in NUCT. __If you are not able__to submit your homework at NUCT, it is ok to submit it by email together with an explanation why NUCT is not possible for you.- Your solution can be either handwritten (tablet or scanned using a scanner or scanner app) or written in LaTeX (feel free to contact me if you want to learn it).
- Please name your file "FirstnameFamilyname_LA2_HWXX.pdf", where XX runs from 01 to 14, to indicate the homework number.

(e.g. if your name is Albert Einstein and you submit Homework 3 you name the file "AlbertEinstein_LA2_HW03.pdf")

**Course schedule****:**The following gives a tentative overview of the topics we will cover each week.

Week 01 (04/20-04/26): Vector spaces (Notes: Lecture 1, Videos: Lecture 1-1 , Lecture 1-2, Homework: HW1)

Week 02 (04/27-05/01): Linear maps (Notes: Lecture 2, Video: Lecture 2, Homework: HW2)

Golden week

Week 03 (05/11-05/17): The matrix of a linear map (Notes: Lecture 3, Video: Lecture 3, Homework: HW3)

Week 04 (05/18-05/24): Determinants & Mathematical induction (Notes: Lecture 4, Video: Lecture 4, Homework: HW4)

Week 05 (05/25-05/31): Properties of the determinant I (Notes: Lecture 5, Video: Lecture 5, Homework: HW5)

Week 06 (06/01-06/07): Properties of the determinant II (Notes: Lecture 6, Video: Lecture 6, Homework: Recall Week 1-6)

Week 07 (06/08-06/14): Eigenvalues and eigenvectors I (Notes: Lecture 7, Video: Lecture 7, Homework: HW6)

Week 08 (06/15-06/21): Eigenvalues and eigenvectors II (Notes: Lecture 8, Video: Lecture 8, Homework: HW7)

Week 09 (06/22-06/28): Eigenvalues and eigenvectors III (Notes: Lecture 9, Video: Lecture 9, Homework: HW8)

Week 10 (06/29-07/05): Applications (Notes: Lecture 10, Video: Lecture 10, Homework: Play around in python)

Week 11 (07/06-07/12): Continuous dynamical systems (Notes: Lecture 11, Video: Lecture 11, Homework: Recall Week 7-10)

Week 12 (07/13-07/19): Linear differential equations I (Notes: Lecture 12, Video: Lecture 12, Homework: HW9)

Week 13 (07/20-07/26): Linear differential equations II (Notes: Lecture 13, Video: Lecture 13, Homework: Prepare for the exam)

Week 14 (07/27-08/02): Review (Review exercises, Video: Lecture 14)

**Final Exam:****7th August**:**17:45 - 19:00 Online via Zoom.****Tutorial schedule:**The tutorial will be done via Zoom meetings each week. The meetings will be every Thursday at 14:45 and meeting IDs are posted in the Facebook group and at the NUCT course.

Last update: 8th August 2020.