ENGG1410-F, Linear Algebra and Vector Calculus

ENGG1410-F Linear Algebra and Vector Calculus

Spring 2019

Professor: Yufei Tao
TAs: Shangqi Lu (sqlu@cse), Hao Xu (haoxu@cse), and Jianwen Zhao (jwzhao@cse)

Quick navigation links:
[Lecture Notes][Tutorials][Exercises][Quizzes and Exams]

Announcements

18. (27 Apr) Final exam statistics posted.

17. (17 Apr) Quiz 3 solutions and statistics posted.

16. (1 Apr) Good news: you will be allowed to bring two pieces of double-sided cheet-sheets into the final exam, namely, one more than previously allowed.

15. (1 Apr) Quiz 3 will take place in the tutorial of 9 Apr. It will start at 4:30pm, and finish at 5pm. The scope includes Lect Notes 10-18. The quiz is open book. You can use a university-approved calculator.

14. (23 Mar) Midterm solutions and statistics posted.

13. (15 Mar) Quiz 2 solutions and statistics posted.

12. (8 Mar) More Midterm Arrangements
- The actual exam time will be 1.5 hours. The exam will start at 2:35pm and end at 4:05pm.
- You can (i) consult a double-sided A4-sized "cheat sheet" and (ii) use a university-approved calculator.
- You can hand-write or type on the cheat sheet.

11. (6 Mar) Midterm Arrangements
- The time is 2:30pm - 4:15pm, 14 March (i.e., the usual Thu lecture time).
- The venue is ELB LT1 (note that this is NOT our usual classroom on Thu).
- The scope covers everything in Lecture 1-10.
- The tutorial of Week 9 (i.e., on 12 March, Tue) will be converted into a lecture. As a result, there will not be a tutorial for Week 9.

10. (1 Mar) I have just released a past midterm paper and its solutions. Remember that we will have our midterm on March 14.

9. (27 Feb) Quiz 2 will take place in the tutorial of 5 Mar. It will start at 4:30pm, and finish at 5pm. The scope includes Lect Notes 4-9. The quiz is open book.

8. (15 Feb) Quiz 1 solutions and statistics posted.

7. (29 Jan) We will start taking attendance this week. As mentioned, it is a faculty requirement that you attend at least 50% of the lectures, counting from Week 4, i.e., this week.

6. (22 Jan) Quiz 1 will take place in the tutorial of 29 Jan. It will start at 4:30pm, and finish at 5pm. The scope includes Lect Notes 1-3, and Section 1 of Lect Notes 4. The quiz is open book.

5. (11 Jan) Grading scheme finalized.

4. (8 Jan) The midterm exam will be organized in the lecture on 14 Mar (which is in Week 9). The scope covers only linear algebra (more on this when the time draws nearer).

3. (8 Jan) There will be three quizzes in this course. They are tentatively scheduled to take place in the tutorials on 29 Jan, 5 Mar, and 9 Apr (which are in Weeks 4, 8, and 12), respectively.

2. (8 Jan) No tutorials in the first week.

1. (5 Jan) Hi all.

Time and Venues

Lectures
Wed, 1:30pm - 2:15pm, Lee Shau Kee, LT3
Thu, 2:30pm - 4:15pm, Lee Shau Kee, LT2

Tutorials
Tue, 4:30pm - 6:15pm, Lee Shau Kee, LT3

Grading Scheme

Tutorial Participation: 3%
Quizzes: 27% (9% each)
Midterm: 30%
Final: 40%

Note 1: It is a faculty requirement that a student needs to attend at least 50% of the lectures (counting from Week 4) in order to obtain a passing grade for the course.

Note 2: In the midterm exam, you will be allowed to consult a double-sided A4-sized "cheat sheet" and use an approved calculator.

Note 3 (new): In the final exam, you will be allowed to consult two pieces of double-sided A4-sized "cheat sheets" and use an approved calculator.

Lecture Notes and Reference Book

The following textbook is a recommended reference for this course:

Erwin Kreyszig. Advanced Engineering Mathematics. 10th Ed., Wiley.

Ownership of the book is not mandatory (but may be beneficial; for example, it contains plenty of exercises). The instructor will make lecture notes available before each class. His notes will cover all the required material, and do not necessarily follow the reference book.

As usual, lecture attendance is vital to gaining thorough understanding.

	Notes	Reference Reading
Lecture 1	Matrix Definitions and Operations	Guide
Lecture 2	Gauss Elimination	Guide
Lecture 3	Ranks	Guide
Lecture 4	Determinants (updated on 23 Jan) Changes: Added in the appendix a proof on sign-flipping in the determinant after switching two rows. Old version	Guide
Lecture 5	More on Linear Systems	Guide
Lecture 6	Inverses	Guide
Lecture 7	Dimensions, Spans, and Linear Transformations	Guide
Lecture 8	Eigenvalues and Eigenvectors	Guide
Lecture 9	Similarity Transformation	Guide
Lecture 10	Orthogonal and Symmetric Matrices	Guide
Lecture 11	Geometry of Vectors	Guide
Lecture 12	Dot Product and Cross Product	Guide
Lecture 13	Vector Derivatives	Guide
Lecture 14	Gradients	Guide
Lecture 15	Curves and Tangent Vectors	Guide
Lecture 16	Surfaces, Tangent Planes, and Surface Normals	Guide
Lecture 17	Arc Lengths	Guide
Lecture 18	Line Integrals by Arc Length	Guide
Lecture 19	Line Integrals by Coordinate and by Dot Product	Guide
Lecture 20	Green's Theorem	Guide
Lecture 21	Path Independence	Guide

There will be no more lecture notes.

Tutorial Material

3% of your overall score will depend on your participation in the tutorials. We will determine your tutorial-participation score as follows. In each tutorial, we will give a number of (usually 3 or 4) questions for you to solve within several minutes. Your (written) solutions will be collected. In the whole semester, if you solve at least 20 questions cumulatively, you will be getting all the 3%. Otherwise, if you solve x < 20 questions, your tutorial-participation score will be (x/20) * 3%.

Week 2: Notes
Week 3: Notes
Week 4: Notes 1 on the permutation-based determinant definition (not testable), and Notes 2
Week 5: Notes 1 and Notes 2 (based on the exercise lists on inverses and linear transformations)
Week 6: Notes 1, Notes 2 on page ranks (not testable), and an interesting site on the geometry of eigenvectors
Week 7: Notes 1 and Notes 2.
Week 8: Notes 1 on quadratic forms (not testable), and Notes 2.
Week 9: No tutorials (because of the midterm).
Week 10: Notes
Week 11: Notes (based on the exercise list on "Line Integrals by Arc Length")
Week 12: Notes (based on the exercise list on "Line Integrals by Coordinate/Dot Product")
Week 13: Notes (based on the exercise list on "Green's Theorem" and "Path Independence")

Exercises

Quizzes and Exams

Quiz 1 Solutions.
Quiz 1 Stats: Mean = 82.6, Standard Deviation = 19.1.

A past midterm paper (solutions; remark: the solution to Question 1(a) is not correct).

Quiz 2 Solutions.
Quiz 2 Stats: Mean = 73.4, Standard Deviation = 24.8.

Midterm (Solutions).
Midterm Stats: Mean = 71.5, Standard Deviation = 20.6, and Top 20 Scores (of this class).

Quiz 3 Solutions.
Quiz 3 Stats: Mean = 82.5, Standard Deviation = 19.0.

Final Exam Stats: Mean = 52.4, Standard Deviation = 22.3, and Top 20 Scores (of this class).