Math 54: Linear Algebra and Differential Equations

Summer 2008, UC Berkeley

Instructor: Scott Armstrong
Email: sarm@math.berkeley.edu
Office: 1041 Evans
Office Hours: Mondays and Tuesdays, 10:30-11:30, and Thursdays, 13:00-14:00
Lectures: Monday - Friday, 08:00-10:00 in 6 Evans

Course Syllabus

Homework #1 (due Friday, June 27): Section 1.1 # 11, 14, 19, 22, 26; Section 1.2 # 3, 11, 14, 15, 16, 33; Section 1.3 # 5, 6, 7, 8, 10, 11, 12, 14, 25; Section 1.4 # 11, 18, 20; Section 1.5 # 7, 12, 25, 26, 29, 30, 31, 32, 35, 39, 40; Section 1.7 # 5, 8, 21, 22, 37, 38. (Also recommended: Section 1.4 # 21, 22, 25, 29-36.)

Homework #2 (due Wednesday, July 2): Section 1.8 # 5, 6, 9, 11, 24, 31, 32; Section 1.9 # 1, 2, 4, 16, 19, 32; Section 2.1 # 5, 8, 11, 17, 23, 24, 25. (Also recommended: Section 1.9 # 33, 34, 35, 36; Section 2.1 # 18, 29, 20, 21, 22.) * Ignore the hint on Section 1.9 # 4, since the hint is wrong. *

Homework #3 (due Tuesday, July 8): Section 2.2 # 3, 4, 8, 13, 14, 15, 16, 17, 32; Section 2.3 # 1, 3, 11, 12, 15, 17, 26, 27, 28; Section 2.8 # 5, 7, 9, 11, 15, 18, 20, 23, 34, 36; Section 2.9 # 3, 5, 9, 10, 13, 15, 22, 24, 26. (Also recommended: Section 2.3 # 18-24, 29-32; Section 2.8 # 31-33, 35; Section 2.9 # 19-21, 23, 25.)

Homework #4 (due Thursday, July 10): Section 3.1 # 9, 10, 12, 41; Section 3.2 # 14, 22, 23, 24, 29, 33, 34, 36; Section 3.3 # 3, 6, 19, 31.

Homework #5 (due Wednesday, July 16): Section 4.4 # 3, 5, 8, 9, 10, 11, 12, 13, 14, 21, 25, 26, 29, 32, 35; Section 4.7 # 1, 2, 5, 7, 8, 15, 16, 19.

Homework #6 (due Friday, July 18): Section 5.1 # 9, 10, 13, 25, 26, 27; Section 5.2 # 1, 6, 10, 13, 23, 24; Section 5.3 # 3, 4, 6, 9, 10, 13, 27.

Homework #7 (due Wednesday, July 23): Section 5.4 # 1, 3, 6, 11, 19, 21, 22; Section 5.5 # 1, 3, 23, 24.

Homework #8 (due Friday, July 25): Section 6.1 # 1, 3, 5, 24; Section 6.2 # 1, 4, 6, 11, 21, 28, 29, 30; Section 6.3 # 3, 5, 6, 8, 9, 12, 15, 24; Section 6.4 # 2, 3, 9; Section 6.5 # 1, 3, 5, 12, 20, 22, 24.

Homework #9 (due Friday, August 1): Section 4.2 # 1, 8, 13, 16, 18, 19, 27, 28, 31; Section 4.3 # 1, 5, 13, 16, 22, 24, 31; Section 4.4 # 9, 12, 16, 19, 22, 26; Section 4.5 # 17, 19, 20, 24, 26, 29. (These are problems from the differential equations book by Nagle, et. al.)

Homework #10 (due Wednesday, August 6): Section 6.2 # 1, 3, 9, 14, 19; Section 9.5 # 12, 13, 31, 33; Section 9.6 # 2, 3, 13, 14.

Homework #11 (due Friday, August 8): Section 10.2 # 2, 4, 9, 14, 15, 18, 19, 21, 28; Section 10.3 # 9, 11, 13, 16 (don't worry about plotting partial sum), 25; Section 10.4 # 1, 7, 9, 13, 15, 17. (Also read, but don't do, Section 10.3 # 33-37.)

Homework #12 (due Wednesday, August 13): Section 10.5 # 1, 4, 6, 11; Section 10.6 # 1, 4, 9, 11; (Suggested problems: Section 10.7 # 1, 3, 7, 11, 19, 20).

Quiz #1 Solution (There is a small error: when I wrote the augmented matrix in problem #1, the (1,1) entry was copied incorrecty as -1 instead of 1; however, this error disappears on the next line, so if you ignore this blunder, then all is well.)

Quiz #2 Solution

Quiz #3 Solution

Quiz #4 Solution

Quiz #5 Solution

Quiz #6 Solution (I made a mistake in calculating one of the eigenspaces on the first problem.)

Quiz #7 Solution

Quiz #8 Solution

Pop Quiz Solution

Quiz #9 Solution

Quiz #10 Solution

Quiz #11 Solution

Quiz #12 Solution

Sample Final Exam. You are advised to attempt Sample Final Exam before you look at the Sample Final Exam Solutions

The Final Exam scores are: 111, 94, 93, 90, 87, 87, 87, 86, 86, 85, 84, 81, 80, 79, 78, 77, 73, 73, 68, 68, 67, 66, 64, 56, 54, 53, 50, 32. The mean is 75.32 and the median is 78.5.

Suggested extra homework problems to work to do when preparing for Midterm #2: Section 6.6 # 1, 4; Section 6.7 # 3, 10, 16, 18; Section 7.1 # 23, 24, 25, 27, 28, 29, 30.

Sample Midterm #2. You are advised to attempt Sample Midterm #2 before you look at the Sample Midterm #2 Solutions

Midterm #2, and the solutions of Midterm #2.

The Midterm #2 scores are: 100, 100, 96, 93, 92, 92, 88, 87, 87, 85, 83, 83, 79, 76, 74, 72, 71, 69, 65, 64, 63, 61, 60, 60, 59, 53, 48, 45, 44, 37, 33. The mean is 71.6, and the median is 72. If I had to choose letter grades based only on this exam, I would say that an A is 92-100, an A-- is 85-88, a B+ is an 83, a B is 74-79, a B-- is 69-72, a C+ is a 63-65, a C is 59-61, a C-- is a 48-53, a D is 44-45, and the scores in the 30s are Fs.

Sample Midterm #1. You are advised to attempt Sample Midterm #1 before you look at the Sample Midterm #1 Solutions

Midterm #1, and the solutions of Midterm #1. Here is another and perhaps better solution of problem 6.

The Midterm #1 scores are: 115, 112, 109, 92, 88, 88, 87, 87, 83, 81, 81, 81, 78, 74, 71, 71, 69, 65, 64, 64, 62, 62, 53, 52, 49, 47, 43, 42, 38, 36, 35, 33. The mean is 69.1, and the median is 70. If I had to choose letter grades based only on this exam, I would say that an A is one of the top 3, an A-- is in the range 87-92, a B+ is 81-83, a B is the 78, a B-- is 69-74, a C+ is a 62-65, a C is 47-53, a C-- is a 42-43, and the scores in the 30s are Ds.

Linear algebra on the internet:

• Linear algebra toolkit - This will be be helpful when you are learning basic matrix manipulations, like finding the inverse or calculating the null space of a matrix A or solving the equation Ax=b. You can type in a problem and it will give you a step-by-step solution.
• Matrix Simulator - A really nice java applet that helps to "visualize" matrices  and think of them as linear transformations. Also helps with visualizing eigenvectors.
• Interactive Data Fitting - Plot points with a mouse click and the java applet will graph the line of best fit for you, using two different ideas of what "best fit" should mean. It Illustrates why the least squares method is "better" than the "least absolute values" method.
• Free linear algebra textbooks available online:
  • Matrix Analysis and Applied Linear Algebra by Carl Meyer
  • Elements of Abstract and Linear Algebra by Edwin Connell

This page was last updated 08/15/2008 at 16:51.