Math 43, Fall 2010
Survey of Linear Algebra
MWF 11:10, XS 303,
Professor Don Davis
- Christmas-Saucon 332, phone 83756, e-mail dmd1
- Office hours: M 8:50-9:50, T Th 2:30-3:30
The text is "Linear Algebra: A Modern Introduction," by Poole, second
edition. (Note, there is a new third edition, but we are not using it.)
The second edition is the one that has been used here the past few years.
Your grade will be determined from the
following, scaled at the end of the semester.
- 100--Quizzes and homework
- 100--First hour exam
- 100--Second hour exam
- 200--Final exam
Quizzes will be unannounced, 5-10 minutes at the end of class approximately once a week.
They will be
composed of problems extremely similar to "suggested problems" assigned
two or three lectures earlier. A small number of "homework problems" will be collected and
graded once a week.
Solutions to suggested (resp. assigned) problems
will be made available on Course Site two days
after they are assigned (resp. late afternoon the day they are due).
No make-up quizzes will be given.
If you have a compelling reason for missing a quiz, present the reason in
writing to your instructor, who may possibly give you an excused absence,
which will result in your receiving an average score on the quiz. It will not
be enough to write "I missed class because I didn't feel well." You will have
to provide some documentation. The main type of excused absence could be if
you are on a Lehigh sports team that has an away game. Half-credit will be
given for just handing in a quiz; this is your reward for attendance.
Late homework will not be accepted; if it is not handed in on the assigned
date and time, a score of zero will be given. If you must miss class on a day
when homework is due, have someone else hand it in for you, or hand it in early.
Quiz and homework scores will be in the same category. The lowest three scores
will be dropped, and the remaining scores averaged.
The hour exams occur during lecture hour. If you
miss an hour exam
for some compelling reason, then contact your instructor within 24 hours of the
exam to explain why you missed the exam. If he accepts your absence as
excused, you will be entitled to take a makeup exam at 4:10
six days after the regular exam was given. No one who takes the
regular exam may take the makeup exam. The final exam will cover material
from the entire semester, with a heavy emphasis on material subsequent to the
second hour exam. You will have three hours for it, but it will only be twice
as long as the hour exams.
Accommodations for Students with Disabilities: If you have a
disability
for which you are or may be requesting accommodations, please contact
both your instructor and the Office of Academic Support Services,
University Center 212 (610-758-4152) as early as possible in the
semester. You must have documentation from the Academic Support
Services office before accommodations can be granted.
Schedule of lectures and homework problems.
- Lecture 1: Monday, August 30: 1.1
- Suggested problems: pp 13-14: 5c, 9, 14, 18, 20.
- Hand in Sept 10: p.56 #2.
- Lecture 2: Wed Sept 1: 1.2
- Suggested problems: pp 26-27: 8, 22, 25, 36, 42, 60.
- Hand in Sept 10: p.27 #54.
- Lecture 3: Fri Sept 3: 1.3
- Suggested problems: pp 41-43: 6, 8b, 12, 14, 16, 22, 26, 30.
- Hand in Sept 10: p 42 #32 with Q changed to [0,2,0].
- Lecture 4: Mon Sept 6: 2.1.
- Suggested problems: pp 64-65: 12, 16, 21, 28, 32.
- Hand in Sept 10: p 64 #34.
- Lecture 5: Wed Sept 8: 2.2
- Suggested problems: p 83: 12, 16, 22, 24, 26.
- Hand in Sept 17: p 84 #25 with x3 in second equation changed to
-x3, the 9 changed to a 5, and the last 4 changed to a 2.
- Lecture 6: Fri Sept 10: 2.2
- Suggested problems: pp 84-85: 31, 34, 42, 46.
- Hand in Sept 17: p 84, #30.
- Lecture 7: Mon Sept 13: 2.3
- Suggested problems: pp 99-100: 4, 8, 12, 16.
- Hand in Sept 17: p 133 #11 with first vector changed to [1 1 2].
- Lecture 8: Wed Sept 15: 2.3, 2.4 (just Allocation of Resources)
- Suggested problems: pp 100-101: 24, 28, 35, 40. p.113 #2 (Show
that there are no solutions. How much would you need to change the
amount of Food C so that there are solutions? What would be the general
solution if this change were made?)
- Hand in Sept 24: p 100, #29 and p 113 #3
- Lecture 9: Fri Sept 17: 2.5 (just Gauss-Seidel method)
- Suggested problems: p. 130: 8 (Omit Jacobi method. Compare
with actual solution), 14.
- Hand in Sept 24: p 130: 11 (Omit Jacobi method. Compare with
actual solution.)
- Lecture 10: Mon Sept 20: 3.1
- Suggested problems: pp 150-151: 4, 6, 8, 20, 26, 32, 36.
- Hand in Sept 24: p 250: 2
- Lecture 11: Wed Sept 22: 3.2, 3.3
- Suggested problems: pp 159-160: 8, 14, 24, 26.
- Hand in Oct 1: p 159: 4
- Lecture 12: Fri Sept 24: 3.3
- Suggested problems: pp 176-177: 6, 24, 26, 38, 40, 54
- Hand in Oct 1: p. 177: 52
- Lecture 13: Mon Sept 27: 3.5
- Suggested problems: pp 207-208: 2, 6, 10, 11, 16
- Hand in Oct 1: p 207: 12 with middle 2 in A changed to 1. Use
your steps to write w as an explicit combination of the rows r1,
r2, and r3 of A.
- Lecture 14: Wed Sept 29: 3.5
- Suggested problems: p 208: 20, 38, 48, 50
- Hand in Oct 15: p 208: 18 with second and third rows interchanged
- Lecture 15: Fri Oct 1: 3.6
- Suggested problems: pp 222: 8, 10, 20
- Hand in Oct 15: p 222: 22.
- Mon Oct 4: Review
- Wed Oct 6: Exam on sections 1.1 to first half of 3.5.
- Lecture 16: Fri Oct 8: 3.7 (Markov)
- Suggested problems: p 244: 6, 8, 9
- Hand in Oct 15: p 244: 11. In (c),
guess and verify.
- Lecture 17: Wed Oct 13: Application to baseball (handout)
(not on exams)
- Hand in Oct 25: problems on handout. (Counts as a whole HW)
- Lecture 18: Fri Oct 15: 3.7 (Population growth)
- Suggested problems: pp 245-246: 20, 24. Remember that L keeps
track of females.
- Hand in Oct 22: p 245: 22 with .1 changed to .2, and 20 changed to 10.
(Hint: What happens after three generations?) Also, explain what the
entries of the original matrix say specifically about survival and birth
of these beetles.
- Lecture 19: Mon Oct 18: 4.1
- Suggested problems: pp 259-260: 6, 12, 14, 20.
- Hand in Oct 22: p 261: 26 with -2 replaced by 4
- Lecture 20: Wed Oct 20: 4.2
- Suggested problems: pp 280-281: 2, 14, 16, 22
- Hand in Oct 29: p 280: 9
- Lecture 21: Fri Oct 22: 4.2
- Suggested problems: p 281-282: 34, 40, 50, 60
- Hand in Oct 29: p 282: 58 with 3 replaced by a variable k, which
can represent any number
- Lecture 22: Mon Oct 25: 4.3
- Suggested problems: pp 295-296: 4, 6, 12, 16
- Hand in Oct 29: p 295: 8 with first row replaced by [2, -1, -2]
- Lecture 23: Wed Oct 27: 4.4
- Suggested problems: pp 306-307: 4, 6, 8
- Hand in Nov 5: p 307: 12
- Lecture 24: Fri Oct 29: 4.4
- Suggested problems: p 307: 16, 20, 24
- Hand in Nov 5: p 307: 18
- Lecture 25: Mon Nov 1: 4.5
- Suggested problems: p 320: 6, 10 (Use k=5)
- Hand in Nov 5: p 320: 11 with 7 replaced by 6. (Use k=5)
- Lecture 26: Wed Nov 3: 4.6 (Markov) pp 322-326
- Suggested problems: p 356: 4, 7
- Hand in Nov 19: p 356: 8 with first column replaced by a column whose
entries are 1/3, 2/3, 0.
- Lecture 27: Fri Nov 5: 4.6 (Population growth) pp 327-329
- Suggested problems: p 356: 14 (Hint: eigenvalue is an integer),
20 (Use calculator or computer to find root of characteristic polynomial)
- Hand in Nov 19: p 356: #19 with 3 changed to 1. (Use calculator or
computer to find root of characteristic polynomial.)
- Lecture 28: Mon Nov 8: Handout on Genetics
- Suggested problem: #1 from genetics handout
- Hand in Nov 19: #1 from genetics handout modified so that AA is
always fertilized with Aa, Aa with AA, and aa with Aa.
- Wed Nov 10: Review
- Fri Nov 12: Exam on Sections 3.5-4.5
- Lecture 29: Mon Nov 15: Handout on Genetics
- Hand in Nov 19: Fertilize with AA, then use the fertilization scheme
of the previous hand-in problem
then repeat, fertilizing again with AA, then the above, etc.
a. Write the transition matrix for a 2-generation transition.
(b). Find the eigenvector whose entries sum to 1.
This will be the limiting distribution after an even number of
transitions. (c) Multiply this vector by the transition matrix for
the AA-fertilization. This will be the limiting distribution after
an odd number of transitions.
- Lecture 30: Wed Nov 17: Matrix of Linear Transformation, Handout.
(available on Course Site).
- Suggested problems: see handout
- Hand in Dec 3: see handout
- Lecture 31: Fri Nov 19: 5.1
- Suggested problems: pp 373-374: 6, 10, 14, 20
- Hand in Dec 3: p 429: 4 (Hint: there are two possible vectors
v_2)
- Lecture 32: Mon Nov 22: 5.2
- Suggested problems: p 384: 6, 8, 18
- Hand in Dec 3: p 384: 14
- Lecture 33: Mon Nov 29: 5.3
- Suggested problems: p 392: 6, 10, 12
- Hand in Dec 3: p 430: 15a with order of vectors reversed, so
that the old x3 becomes the new x1, etc.
- Lecture 34: Wed Dec 1: 5.4
- Suggested problems: pp 404-405: 2, 6, 20, 22
- Hand in Dec 10: p 405: 21 with the 2 changed to a 3.
- Lecture 35: Fri Dec 3: 7.3
- Suggested problems: p 595: 8 (Also, graph the points and the
line); p 596: 20 (Also, compute Ax for
your
solution and compare with b)
- Hand in Dec 10: p 596: 12 (Also, graph the points and the line.)
- Lecture 36: Mon Dec 6: 7.3
- Suggested problem: p. 596: 16 (Change last point to (4,0). Also,
compare values on curve with data points.)
- Hand in Dec 10: p 596: 26. (Also, compare
values.)
- Lecture 37: Wed Dec 8: Google algorithm, handout
- Fri Dec 10: Review