Math 54: Linear Algebra and Differential Equations. Fall 2018.

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

Section: TTh, see list for times

Office Hours: Monday 6:40-8:00pm and Wednesday 12:20-2:00pm (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 in-class 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.

  1. HW1 solutions (problems assigned W 8/22).
  2. HW2 solutions (problems assigned M 8/27 and W 8/29).
  3. HW3 solutions (problems assigned W 9/5).
  4. HW4 solutions (problems assigned M 9/10 and W 9/12).
  5. HW5 solutions (problems assigned M 9/17) .
  6. HW6 solutions (problems assigned W 9/26 ) .
  7. HW7 solutions (problems assigned M 10/1 and W 10/3) .
  8. HW8 solutions (problems assigned M 10/8 and W 10/10) .
  9. HW9 solutions (problems assigned M 10/15 and W 10/17) .
  10. HW10 solutions (problems assigned M 10/22 and W 10/24) .
  11. HW11+12 solutions (problems assigned M 10/29 and M 11/5) . correction: 7.4.11 should be |det(A)| not det(A).
  12. HW13 solutions (problems assigned M 11/12 and M 11/14) .
  13. HW14 solutions (problems assigned 11/19 ) .
  14. HW15 solutions (problems assigned 11/26 ) .


Announcements


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.

#DateTopics ReadingsHomework problemsRemarks
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, linear transformations 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 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 M 9/17 subspaces, basis, dimension, rank 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 5.1-5.3 5.1:5,7,13,20,21,22,23,24,25,26,29,31.
5.2:7,9,19,21.
+watch this video
15 M 10/15 diagonalization 5.3-5.5 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 gram-schmidt, least squares, inner product spaces 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.
4.2:27-35 are optional
bc they were assigned late
but highly recommended
22 W 11/7 second order ODE with complex roots, inhomogeneous ODE 4.3-4.5 (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, PDE 9.6, 9.7, 10.1, 10.2 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), 10.3-4 6.7: 9,13,25.
10.3: 1,5,7,9,11,28.
10.4:1,3,6.
square wave animation
cool article.
26 W 11/28 finish svd, review 7.4(lay) no homework
Friday 12/14 Final Exam 3pm--6pm (in Wheeler 150)