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: MW 5:006:30pm, Wheeler 150.
Section: TTh, see list for times
Office Hours: Monday 6:408:00pm and Wednesday 12:202:00pm (1035 Evans)
Course Control Number: 22247
Piazza signup
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:
Graduate Student Instructors and office hours. You can attend any GSI's office hours.
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 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 inclass midterm exams on Monday, 9/24, and Wednesday, 10/31. There will be no makeup exams, except for documented medical emergencies.
Quizzes will be held in section every Tuesday. They will cover material up to the preceding Wednesday. 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 will be collected the following Tuesday in section on Gradescope by 11:59pm on Tuesday. If you have not already been added, the entry code for this course's Gradescope is M6Z5YJ 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.
Announcements
#  Date  Topics  Readings  Homework problems  Remarks 
1  W 8/22  intro, linear equations, row echelon form  1.1, 1.2  1.1: 1,3,5,7,11,15,20,23,24,28.  
2  M 8/27  row reduction  1.2, 1.3  1.2: 1,5,7,11,15,23,26,30.  
3  W 8/29  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. 

*  M 9/3  holiday  
4  W 9/5  solution sets, linear independence, 
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  M 9/10  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  W 9/12  11 and onto transformations, matrix algebra, inversion  1.9, 2.12.3  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  M 9/17  subspaces, basis, dimension, 
2.8, 2.9  2.8: 2,4,5,12,13,22,23,27,31,34. 2.9: 2,6,7,9,17,27,28. 

8  W 9/19  review and applications  blog post 

9  M 9/24  Midterm 1 (in class)  Ch. 1 and 2  
10  W 9/26  rank, vector spaces  4.1  4.1: 1, 2, 5, 6, 8, 11, 20, 21, 22, 23, 31, 32  
11  M 10/1  linear transformations, bases, coordinates  4.2end, 4.3, 4.4  4.2: 30,31,33,35. 4.3: 26,31,32,33. 4.4: 15,22,23,24,25,31,32. 

12  W 10/3  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. 

13  M 10/8  change of basis, determinants  4.7, 3.1,3.2  4.7:1,3,5,7,11,13,15,20a. 3.1:5,11,22,31,33. 3.2:3,7,17,21,27,28,29,32,33,34.. 

14  W 10/10  eigenvalues, eigenvectors, diagonalization  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 

15  M 10/15  diagonalization  5.35.5  5.3: 5,8,13,14,21,22,23,27,31,32 5.4: 11,13,17,23 
guest lecture by Prof. Gu 
16  W 10/17  similarity, complex eigs, applications  5.5  5.4: 13,17,19,20,21,22,24 5.5:3,9,13,17,22,23,24,25. read this article on universality 

17  M 10/22  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. 

18  W 10/24  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. 

19  M 10/29  symmetric matrices, svd, review  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. + read this article on image compression 

W 10/31  Midterm 2 (in class)  
21  M 11/5  First and second order homogeneous ODE  4.1,4.2 (NS and S)  4.1: 2,3,4,5. 4.2: 1,5,15,27,29,34,35. 
4.2:2735 are optional bc they were assigned late but highly recommended 
22  W 11/7  second order ODE with complex roots, inhomogeneous ODE  4.34.5 (NS and S)  no homework  
*  M 11/12  holiday  4.3:1,15,23,28,30. 4.4:9,11,12,13,18. 4.5:1,2,,12,20,27. 

23  W 11/14  systems of ODE  9.1,9.4,9.5 (NS and S)  9.4: 3,7,13,16,19,23,27 9.5:13,17,21,31,35 

24  M 11/19  inhomogeneous systems of ODE, 
9.6, 9.7, 
9.6: 1,7,13,15. 9.7: 1,4,8. 
video lecture part 1(Prof. Paulin, complex eigs) part 2(summary of ODE) part 3(mass spring systems) 
*  W 11/21  holiday  
25  M 11/26  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. 
26  W 11/28  finish svd, review  7.4(lay)  no homework  
Friday 12/14  Final Exam 3pm6pm (in Wheeler 150) 