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, Wheeler 150.
Section: MWF, see list for times
Office Hours: W 56:30pm, Th 12:302pm (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:
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 inclass 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
#  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  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: 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. 13  
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. 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. 

15  T 3/10  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 3/12  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 3/17  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  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 4/2  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  4.34.5 (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), 10.34  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 4/30  finish fourier series, review  10.34  fourier sound demo 