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 5:006:30pm, on Zoom (link on bCourses).
Section: MWF, see list for times
Office Hours:T 12pm or F 45pm on Zoom
Course Control Number: 25957
Piazza signup
Gradescope: If you have not already been added, the entry code for this course's Gradescope is D5K2Y6 at gradescope.com. For instructions on how to scan and upload your hw on Gradescope, see this video and handout.
List of GSI's and Office Hours: see bCourses or Piazza for office hours and zoom links. Any student can attend any GSI's office hours.
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 the Mathematics undergraduate advisor Jennifer Sixt, 964 Evans, jensixt@math.obvious.edu
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 two HW and Quiz grades will be dropped, and the lower midterm score will be replaced by the final, if it helps. All quizzes and exams are open book and based on an honor code. Scores will not be curved so you do not have to worry about competing with others, and can focus on learning the material and showing me and the GSIs that you understand it. 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 takehome 36 hour midterm exams on Gradescope, on Thursday, 2/18, and Tuesday, 4/6. There will be no makeup exams, except for documented medical emergencies.
Takehome 24 hour Quizzes will be held on Gradescope every Wednesday. They will cover material up to the preceding Thursday. The quizzes will be of roughly the same difficulty as the exams, and are the best way to check your understanding of the material.
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. Homework will be corrected on a 0/1/2 scale for completeness. Homework solutions will be posted on Wednesdays in bCourses under 'files'.
Announcements
#  Date  Topics  Readings  Homework problems  Remarks 
1  T 1/19  intro, linear equations, existence and uniqueness  Lay 1.1  Lay 1.1: 1,3,5,7,11,15,20,23,24,28.  
2  Th 1/21  row echelon form, row reduction  1.2, 1.3  1.2: 1,5,7,11,15,23,26,30.  
3  T 1/26  vectors, linear combinations, span, column 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 1/28  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 2/2  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 2/4  11 and onto transformations, matrix algebra, 
1.9, 2.12.3  1.9: 29, 30. 2.1: 1,10,12,15,18,22,23,31,32. 

7  T 2/9  inverse, determinant  2.2, 2.3, 3.1,3.2  2.2: 10, 16, 20, 24, 30, 32. 2.3: 2 , 5, 12, 15, 21, 28, 36. 3.1:5,11,22,31,33. 3.2:3,7,17,21,27,28,29,32,33,34 

8  Th 2/11  subspaces, basis, dimension,  2.8, 2.9  2.8: 2,4,5,12,13,22,23,27,31,34. 2.9: 

9  T 2/17  review and applications  [xkcd] word2vec paper word2vec demo 

10  Th 2/18  Midterm 1  Ch. 13  
11  T 2/23  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 2/25  bases, coordinates  4.3, 4.4  4.3: 26,31,32,33. 4.4: 15,22,23,24,25,31,32. 

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

14  Th 3/4  change of basis  4.7  4.7:1,3,5,7,11,13,15,20a.  
15  T 3/9  eigenvalues, eigenvectors  5.15.3  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 3/11  similarity, diagonalization  5.35.5  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 3/16  complex eigenvalues, applications  5.5  5.5:3,9,13,17,22,23,24,25. read this article on universality 

18  Th 3/18  geometry of R^n  6.1,6.2,6.3  6.1:11,13,15,19,21,24,27,28,30,31. 6.2:3,11,13,23,25,26. 6.3:3,7,13,16,20,21,24. 

19  T 3/30  gramschmidt, 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 4/1  projections, row rank=col rank, review  lecture notes  no HW  
21  T 4/6  Midterm 2 (online, no lecture)  Ch. 17  
22  Th 4/8  symmetric matrices, svd  7.1,7.4  7.1:9,10,17,19,23,25,26,28,29,30,31,35.  
23  T 4/13  finish svd, first and second order homogeneous ODE  7.4 (Lay), 4.1,4.2 (NS and S) 
7.4:5,13,17,18,19. 4.1: 2,3,4,5. 4.2: 1,5,15,27,29,34,35. 
article on image compression Nikhil's notes 
24  Th 4/15  more on SVD (guest lecture), second order ODE  4.2 (NS and S)  spring simulator Nikhil's notes 

25  T 4/20  systems of ODE  9.1,9.4,9.5 (NS and S)  4.3:1,15,23,28,30. 4.5:1,2,,12,20,27. 9.4: 3,7,13,16,19,23,27 9.5:13,17,21,31,35 
Nikhil's notes 
26  Th 4/22  systems of ODE  9.6, 9.8  9.6: 1,7,13,15.  
27  T 4/27  inner product spaces, fourier series  6.7(lay), 10.34  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 4/29  finish fourier series  10.34  fourier sound demo 