Math 54

Math 54: Linear Algebra and Differential Equations. Spring 2020.

Course description: Basic linear algebra; matrix arithmetic and determinants. Vector spaces; inner product spaces. Eigenvalues and eigenvectors; linear transformations; symmetric matrices and SVD. Homogeneous ordinary differential equations; Fourier series and partial differential equations.

Instructor: Nikhil Srivastava, email: firstname at math.obvious.edu

Please come to office hours or consult with your GSI before sending me email about logistical concerns. As far as possible, please use Piazza for mathematical questions.

Lectures: TTh 5:00-6:30pm, Wheeler 150.

Section: MWF, see list for times

Office Hours: W 5-6:30pm, Th 12:30-2pm (1035 Evans)

Course Control Number: 20365

Piazza signup

List of GSI's and Office Hours: txt

Enrollment Issues: Unfortunately, I have no control over enrollment issues. If you have any concerns about the waitlist, switching sections, and so on, please contact the registrar or one of the Mathematics undergraduate advisors:

Thomas Brown, 965 Evans, brown@math.obvious.edu
Jennifer Sixt, 964 Evans, jensixt@math.obvious.edu

Online Guidelines, describing how the course will be delivered online

Textbook:Linear Algebra and Differential Equations, ~~Second~~ Third Custom Edition for UC Berkeley, by Lay, Nagle, Saff and Snider (includes 5e of Lay and 9e of NSS). picture of the cover

Grading: 5% HW, 15% quizzes, 20% x 2 midterms, 40% final. The bottom three HW and Quiz grades will be dropped, and the lower midterm score will be replaced by the final, if it helps. All exams will be curved. The median grade will be at least a B-. This is not an upperbound; if everyone does extremely well, I will be happy to give everyone an A+.

Exams: There will be two in-class midterm exams on Thursday, 2/20, and Tuesday, 4/7. There will be no makeup exams, except for documented medical emergencies.

Quizzes will be held in section every Wednesday. They will cover material up to the preceding Thursday. The quizzes will be substantially easier than the exams, are and designed to regularly check basic understanding of the material, so that you know in case you are falling behind.

Homework will be assigned daily (problems from the textbook+occasional extra problems) on this webpage, and each week's homework (i.e., both Tuesday's and Thursday's problems, from the webpage) will be collected the following Tuesday on Gradescope by 11:59pm on Tuesday, in a single gradescope assignment. If you have not already been added, the entry code for this course's Gradescope is 9BRB4G at gradescope.com. For instructions on how to scan and upload your hw on Gradescope, see this video and handout. Homework will be corrected on a 0/1/2 scale for completeness. Homework solutions will be posted on Wednesdays in bCourses under 'files'.

Announcements

(1/21). Welcome to the class! The first section is on Friday 1/24
(1/23). Quizzes will be held on Wednesday in section. So the next quiz is on 1/29.
(2/3). Section 214 and 215 (2-3 and 3-4pm) will take place starting today in 85 and 87 Evans respectively, with GSI Yash Somaiya.
(2/6) Since I didn't get to explain the algorithm for computing the inverse of a matrix today, I have moved three problems (2.2: 10,30,32) to the next homework.
(2/10) HW solutions will now be posted on bCourses, not on this webpage.
(2/13) Practice MT1 #1 and solutions.
(2/13) Practice MT1 #2 and solutions.
(2/13) Practice MT1 #3 and solutions. correction: the answer to Q5 should be -(1/2)v_3-(1/2)v_4
(2/13) Study sheet for Midterm 1.
(2/13) For a short introduction to set theoretic notation, see Appendix A of these notes by Prof. Hutchings.
(2/17) There will be no quiz on Wednesday, 2/19, the day before the midterm.
(2/18) My office hours this week are moved to 11-1230 and 630-8pm TODAY.
(3/12) My second office hours this week are moved to F 630-8pm on Zoom.
(3/16) HW7 will now be due on Gradescope on friday instead of tuesday.

Class Schedule

This course covers a lot of material very quickly, and in order to digest it you will have to read the assigned sections before lecture.

# Date Topics Readings Homework problems Remarks

1 T 1/21 intro, linear equations 1.1 1.1: 1,3,5,7,11,15,20,23,24,28.
2 Th 1/23 row echelon form, row reduction 1.2, 1.3 1.2: 1,5,7,11,15,23,26,30.

3 T 1/28 linear combinations, span, column picture, matrix picture 1.3, 1.4 1.3: 1,5,9,11,14,23,24,29,32
1.4: 1, 4, 11, 13, 15, 24, 25, 29, 30, 31, 34.

4 Th 1/30 linear independence, solution sets 1.5, 1.7 1.5: 1,5,9,23,24,25,38,39.
1.7: 1, 7, 9, 11,21, 22, 31, 32, 33, 34, 37, 38.

5 T 2/4 linear transformations, the matrix of a linear transformation 1.8, 1.9 1.8: 1,4,8,12,14,16,17,22,24,31,32.
1.9: 4,6,9,23abcd,33,36.

6 Th 2/6 1-1 and onto transformations, matrix algebra, inversion 1.9, 2.1-2.3 1.9: 29, 30.
2.1: 1,10,12,15,18,22,23,31,32.
2.2: 10, 16, 20, 24, ~~30, 32~~.
2.3: 2 , 5, 12, 15, 21, 28, 36.

7 T 2/11 subspaces, basis, dimension, 2.8, 2.9 2.2: 10, 30, 32.
2.8: 2,4,5,12,13,22,23,27,31,34.
2.9: 2,6,7,9,17,27,28.

8 Th 2/13 determinants 3.1,3.2 3.1:5,11,22,31,33.
3.2:3,7,17,21,27,28,29,32,33,34

9 T 2/18 review and applications

10 Th 2/20 Midterm 1 (in class) Ch. 1-3

11 T 2/25 vector spaces, linear transformations 4.1, 4.2 4.1: 1, 2, 5, 6, 8, 11, 20, 21, 22, 23, 31, 32
4.2: 30,31,33,35.

12 Th 2/27 bases, coordinates 4.3, 4.4 4.3: 26,31,32,33.
4.4: 15,22,23,24,25,31,32.

13 T 3/3 dimension, the matrix of a linear trans, change of basis 4.5, 5.4 first 2 sec 4.5: 9,11,19,21,23,25,26,27,29,31,32.
~~4.7:1,3,5,7,11,13,15,20a.~~
5.4:1,3,5,9.

14 Th 3/5 change of basis 4.7 4.7:1,3,5,7,11,13,15,20a.
~~5.1:5,7,13,20,21,22,23,24,25,26,29,31.~~
~~5.2:7,9,19,21.~~

15 T 3/10 eigenvalues, eigenvectors 5.1-5.3 5.1:5,7,13,20,21,22,23,24,25,26,29,31.
5.2:7,9,19,21.

+watch this video

16 Th 3/12 similarity, diagonalization 5.3-5.5 5.3: 5,8,13,14,21,22,23,27,31,32
5.4: 11,13,17,23,19,20,21,22,24

17 T 3/17 complex eigenvalues, applications, begin orthogonality 5.5, 6.1
5.5:3,9,13,17,22,23,24,25.
read this article on universality
6.1:11,13,15,19,21,24,27,28,30,31.

18 Th 3/19 geometry of R^n 6.1,6.2,6.3
6.2:3,11,13,23,25,26.
6.3:3,7,13,16,20,21,24.

19 T 3/31 gram-schmidt, least squares 6.4,6.5 6.4:3,9,17ab,18ab.
6.5:3,5,7,17,19,20,21,22.
6.6:1,7.

20 Th 4/2 projections, row rank=col rank, review lecture notes no HW

21 T 4/7 Midterm 2 (online, no lecture)

22 Th 4/9 symmetric matrices, svd 7.1,7.4 7.1:9,10,17,19,23,25,26,28,29,30,31,35.
7.4:5,13,17,18,19.

23 T 4/14 finish svd, first and second order homogeneous ODE 7.4, 4.1,4.2 (NS and S) 4.1: 2,3,4,5.
4.2: 1,5,15,27,29,34,35. article on image compression

24 Th 4/16 second order ODE with complex roots, inhomogeneous ODE 4.3-4.5 (NS and S) 4.3:1,15,23,28,30. spring simulator

25 T 4/21 systems of ODE 9.1,9.4,9.5 (NS and S)
4.4:9,11,12,13,18.
4.5:1,2,,12,20,27.
9.4: 3,7,13,16,19,23,27
9.5:13,17,21,31,35

26 Th 4/23 inhomogeneous systems of ODE 9.6, 9.7, 9.6: 1,7,13,15.
(9.7: 1,4,8. optional)

27 T 4/28 inner product spaces, fourier series 6.7(lay), 10.3-4 6.7: 9,13,25.
10.3: 1,5,7,9,11,28.
10.4:1,3,6. square wave animation
cool article.

28 Th 4/30 finish fourier series, review 10.3-4 fourier sound demo

#	Date	Topics	Readings	Homework problems	Remarks
1	T 1/21	intro, linear equations	1.1	1.1: 1,3,5,7,11,15,20,23,24,28.
2	Th 1/23	row echelon form, row reduction	1.2, 1.3	1.2: 1,5,7,11,15,23,26,30.
3	T 1/28	linear combinations, span, column picture, matrix picture	1.3, 1.4	1.3: 1,5,9,11,14,23,24,29,32 1.4: 1, 4, 11, 13, 15, 24, 25, 29, 30, 31, 34.
4	Th 1/30	linear independence, solution sets	1.5, 1.7	1.5: 1,5,9,23,24,25,38,39. 1.7: 1, 7, 9, 11,21, 22, 31, 32, 33, 34, 37, 38.
5	T 2/4	linear transformations, the matrix of a linear transformation	1.8, 1.9	1.8: 1,4,8,12,14,16,17,22,24,31,32. 1.9: 4,6,9,23abcd,33,36.
6	Th 2/6	1-1 and onto transformations, matrix algebra, inversion	1.9, 2.1-2.3	1.9: 29, 30. 2.1: 1,10,12,15,18,22,23,31,32. 2.2: 10, 16, 20, 24, ~~30, 32~~. 2.3: 2 , 5, 12, 15, 21, 28, 36.
7	T 2/11	subspaces, basis, dimension,	2.8, 2.9	2.2: 10, 30, 32. 2.8: 2,4,5,12,13,22,23,27,31,34. 2.9: 2,6,7,9,17,27,28.
8	Th 2/13	determinants	3.1,3.2	3.1:5,11,22,31,33. 3.2:3,7,17,21,27,28,29,32,33,34
9	T 2/18	review and applications
10	Th 2/20	Midterm 1 (in class)	Ch. 1-3
11	T 2/25	vector spaces, linear transformations	4.1, 4.2	4.1: 1, 2, 5, 6, 8, 11, 20, 21, 22, 23, 31, 32 4.2: 30,31,33,35.
12	Th 2/27	bases, coordinates	4.3, 4.4	4.3: 26,31,32,33. 4.4: 15,22,23,24,25,31,32.
13	T 3/3	dimension, the matrix of a linear trans, change of basis	4.5, 5.4 first 2 sec	4.5: 9,11,19,21,23,25,26,27,29,31,32. ~~4.7:1,3,5,7,11,13,15,20a.~~ 5.4:1,3,5,9.
14	Th 3/5	change of basis	4.7	4.7:1,3,5,7,11,13,15,20a. ~~5.1:5,7,13,20,21,22,23,24,25,26,29,31.~~ ~~5.2:7,9,19,21.~~
15	T 3/10	eigenvalues, eigenvectors	5.1-5.3	5.1:5,7,13,20,21,22,23,24,25,26,29,31. 5.2:7,9,19,21. +watch this video
16	Th 3/12	similarity, diagonalization	5.3-5.5	5.3: 5,8,13,14,21,22,23,27,31,32 5.4: 11,13,17,23,19,20,21,22,24
17	T 3/17	complex eigenvalues, applications, begin orthogonality	5.5, 6.1	5.5:3,9,13,17,22,23,24,25. read this article on universality 6.1:11,13,15,19,21,24,27,28,30,31.
18	Th 3/19	geometry of R^n	6.1,6.2,6.3	6.2:3,11,13,23,25,26. 6.3:3,7,13,16,20,21,24.
19	T 3/31	gram-schmidt, least squares	6.4,6.5	6.4:3,9,17ab,18ab. 6.5:3,5,7,17,19,20,21,22. 6.6:1,7.
20	Th 4/2	projections, row rank=col rank, review	lecture notes	no HW
21	T 4/7	Midterm 2 (online, no lecture)
22	Th 4/9	symmetric matrices, svd	7.1,7.4	7.1:9,10,17,19,23,25,26,28,29,30,31,35. 7.4:5,13,17,18,19.
23	T 4/14	finish svd, first and second order homogeneous ODE	7.4, 4.1,4.2 (NS and S)	4.1: 2,3,4,5. 4.2: 1,5,15,27,29,34,35.	article on image compression
24	Th 4/16	second order ODE with complex roots, inhomogeneous ODE	4.3-4.5 (NS and S)	4.3:1,15,23,28,30.	spring simulator
25	T 4/21	systems of ODE	9.1,9.4,9.5 (NS and S)	4.4:9,11,12,13,18. 4.5:1,2,,12,20,27. 9.4: 3,7,13,16,19,23,27 9.5:13,17,21,31,35
26	Th 4/23	inhomogeneous systems of ODE	9.6, 9.7,	9.6: 1,7,13,15. (9.7: 1,4,8. optional)
27	T 4/28	inner product spaces, fourier series	6.7(lay), 10.3-4	6.7: 9,13,25. 10.3: 1,5,7,9,11,28. 10.4:1,3,6.	square wave animation cool article.
28	Th 4/30	finish fourier series, review	10.3-4	fourier sound demo