Course description: Basic linear algebra; matrix arithmetic and determinants. Vector spaces; inner product spaces. Eigenvalues and eigenvectors; linear transformations. Homogeneous ordinary differential equations; firstorder differential equations with constant coefficients. 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: MWF 4:005:00pm, 155 Dwinelle.
Office Hours: Monday 5:156:30pm (1035 Evans) and Tuesday 2:003:45pm (Student Learning Center)
Course Control Number: 31371
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
Textbook:Linear Algebra and Differential Equations, Second Custom Edition for UC Berkeley, by Lay, Nagle, Saff and Snider.
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 Friday, 9/23, and Monday, 10/31. There will be no makeup exams, except for documented medical emergencies.
Quizzes will be held in section every Friday. They will cover material up to the preceding Wednesday. There will be no quiz on midterm days. 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) on this webpage, and each week's homework will be collected the following Wednesday in section.
Announcements
1
#  Date  Topics  Readings  Homework problems  Remarks 
1  W 8/24  Intro, linear equations  1.1  1,3,5,7,11,15,20,23,24,28.  
2  F 8/26  Row reduction  1.2  1,5,7,11,15,23,26,30.  Quiz on Complex numbers in section 
3  M 8/29  The column picture  1.3  1,5,9,11,14,23,24,29 

4  W 8/31  Matrix equations and solution sets  1.41.5  1.4: 11, 13, 15, 24, 25, 29, 30, 31, 34. 1.5: 1, 5, 9, 24, 25x, 38, 39 
x means optional, but recommended 
5  F 9/2  Linear independence  1.7  1, 7, 9, 11, 22, 31, 32, 33, 34, 37, 38.  
*  M 9/5  Labor Day  
6  W 9/7  Linear Transformations  1.8  2, 8, 12, 14, 16, 17, 22, 30, 31, 32.  
7  F 9/9  The Matrix of a Linear Transformation  1.9  2, 4, 6, 9, 19, 22, 26, 33x, 35, 36.  
8  M 9/12  Matrix Algebra 
2.1  2.1: 1,2,10,12,15,18,22,23,31,32.  
9  W 9/14  Inverses and how to compute them  2.2, 2.3  2.2: 10, 12, 13, 16, 20, 22, 24, 30, 32. 2.3: 2 , 5, 8, 12, 15, 21, 28, 36. 

10  F 9/16  Subspaces and Bases  2.6  2, 5, 7, 11, 13, 18, 22, 24, 27, 28, 34.  
11  M 9/19  Dimension and Rank  2.7  3,5,7,9,16,21,23,24.  
12  W 9/21  Review  Ch 1 and 2  
13  F 9/23  Midterm 1 (in class)  see Announcements for study materials  
14  M 9/26  Vector Spaces  4.1  1, 2, 5, 6, 8, 11, 20, 21, 22, 23, 31, 32.  
15  W 9/28  Span, Linear independence, Basis  4.3, 4.4  4.3: 26, 33, 34, 37x 4.4: 13, 14, 18, 19x, 20 Ch4 Supplementary: 4, 5, 6, 8.  
16  F 9/30  Coordinates, Linear Transformations, Kernel and Image  4.2end, 4.4  4.2: 30, 31, 33x, 35, 36x 4.3: 31, 32, 33 4.4: 22, 23, 24, 26, 28, 31, 32. 
Only the last part of 4.2 is new the rest is a review of Null and Col. 
17  M 10/3  The Matrix of a Linear Transformation  5.4, first 2 sec  4.5: 21, 23 5.4: 2, 6, 9. 

18  W 10/5  Change of Basis, Dimension  4.5, 4.7  4.7: 3, 7, 8, 13, 14, 20a. 4.5: 9, 11, 25, 26, 27, 30, 31x 

19  F 10/7  Determinants  3.1, 3.2  3.1: 4, 22, 25, 38, 43x 3.2: 6, 7, 16, 22, 27, 29, 32, 33x, 34. 

20  M 10/10  Eigenvalues and Eigenvectors  5.1, 5.2  5.1: 2, 7, 16, 20, 21, 24, 25, 29, 32. 5.2: 4, 10, 19. 

21  W 10/12  Diagonalization  5.3  5.3: 5, 8, 13, 14, 21, 27, 31, 32. 5.4: 11, 14, 17, 23. 

22  F 10/14  More Diagonalization, Applications  5.4  5.3: 2, 3, 4, 5, 22, 24, 25, 29. Supplementary: 2, 9, 10x. 
American Scientist article 
23  M 10/17  Complex Eigenvalues, Applications  5.5  5.5: 1, 4, 8, 12, 13, 22, 25.  
24  W 10/19  Geometry of R^n  6.1, 6.2  6.1: 2, 6, 7, 10, 14, 17, 19, 24, 27, 29. 6.2: 5, 9, 23abc, 32. 

25  F 10/21  Orthogonal Projections  6.3  6.1: 30 6.3: 1, 4, 8, 12, 14, 19, 22, 24. 

26  M 10/24  GramSchmidt and Least Squares  6.4, 6.5  6.4: 2, 6, 10, 17ab, 22 6.5: 3, 5, 7, 9, 17 , 19, 22. 

27  W 10/26  Inner Product Spaces  6.7  1, 7, 10, 14, 16, 18, 22, 26.  
28  F 10/28  Symmetric Matrices, review  7.1  
M 10/31  Midterm 2 (in class)  
30  W 11/2  Intro to Diff Eq, First and Second Order Homogeneous DE  4.1, 4.2  7.1(Lay): 1, 17, 26, 27, 29 4.1: 1,2 4.2: 3, 5, 10, 13 

31  F 11/4  2nd order ODE with complex and repeated roots  4.2, 4.3  4.3: 3, 13, 22, 28, 30, 32, 36.  
32  M 11/7  Inhomogeneous equations, method of undetermined coeffs  4.4, 4.5  4.4: 1, 2, 3, 11, 12, 21, 29. 4.5: 2, 5, 18, 20. 

33  W 11/9  Systems of linear ODE  9.1, 9.4  9.1: 3, 7, 10 9.4: 3, 5, 7, 26, 27 

34  M 11/14  Homogeneous Systems of linear ODE  9.4, 9.5  9.4: 20x, 21, 23, 28, 37 9.5: 19, 21, 31, 32, 45x. 

35  W 11/16  Complex roots, nonhomogeneous systems  9.6, 9.7  9.4: 20(skip if you did it last week), 31 9.6: 3, 5, 13ac, 20x. 9.7: 2,8. 
(optional) Read 9.8. It's cool. 
36  F 11/18  Intro to Partial Differential Eqns  10.1, 10.2  Guest Lecture by Prof. Lin  
37  M 11/21  The Heat Equation, Eigenfunctions  10.2  10.2: 1 ,3 ,5 ,9 , 12, 15, 16.  
38  M 11/28  Fourier Series solution of the heat equation  10.3, 10.4  10.4: 5, 7, 8, 10, 17, 19.  Videos: heat equation , sawtooth, square wave. 
39  W 11/30  Fourier Series  10.3, 10.4  10.3: 1, 5, 9, 14, 15.  cool article. 
40  F 12/2  Review  NS and S  
Th 12/15  Final Exam 8am11am (in 155 Dwinelle) 