Math 43, Fall 2009

Survey of Linear Algebra

Christmas-Saucon 332, phone 83756, e-mail dmd1
Office hours: M 9:30-10:30, T Th 2:30-3:30

The text is "Linear Algebra: A Modern Introduction," by Poole, second edition. 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 once or twice most weeks. They will be composed of problems extremely similar to homework 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 Blackboard under Assignments two days after they are assigned (resp. the day after 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. 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 24: 1.1
- Suggested problems: pp 13-14: 5c, 9, 14, 18, 20.
- Hand in Sept 4: p.56 #4.
Lecture 2: Wed Aug 26: 1.2
- Suggested problems: pp 26-27: 8, 22, 25, 36, 42, 60.
- Hand in Sept 4: p.26 #30.
Lecture 3: Fri Aug 28: 1.3
- Suggested problems: pp 41-43: 6, 8b, 12, 14, 16, 22, 26, 30.
- Hand in Sept 4: p 42 #32.
Lecture 4: Mon Aug 31: 2.1.
- Suggested problems: pp 64-65: 12, 16, 21, 28, 32.
- Hand in Sept 4: p 64 #30.
Lecture 5: Wed Sept 2: 2.2
- Suggested problems: p 83: 12, 16, 22, 24, 26.
- Hand in Sept 11: p 84 #25 (show your work).
Lecture 6: Fri Sept 4: 2.2
- Suggested problems: pp 84-85: 31, 34, 42, 46.
- Hand in Sept 11: p 133 #4.
Lecture 7: Mon Sept 7: 2.3
- Suggested problems: pp 99-100: 4, 8, 12, 16.
- Hand in Sept 11: p 100: #10.
Lecture 8: Wed Sept 9: 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 18: p 113 #4
Lecture 9: Fri Sept 11: 2.5 (just Gauss-Seidel method)
- Suggested problems: p. 130: 8 (Iterate until differences are less than 0.1. Omit Jacobi method), 14.
- Hand in Sept 18: p 130: 12 (Iterate until differences are less than 0.01. Omit Jacobi method).
Lecture 10: Mon Sept 14: 3.1
- Suggested problems: pp 150-151: 4, 6, 8, 20, 26, 32, 36.
- Hand in Sept 18: p 150: 16
Lecture 11: Wed Sept 16: 3.2
- Suggested problems: pp 159-160: 8, 14, 24, 26.
- Hand in Sept 25: p 160: 28
Lecture 12: Fri Sept 18: 3.3
- Suggested problems: pp 176-177: 6, 24, 26, 38, 40, 54
- Hand in Sept 25: p. 177: 58
Lecture 13: Mon Sept 21: 3.4
- Suggested problems: pp 187-188: 8, 10.
- Hand in Sept 25: p 251: 12
Lecture 14: Wed Sept 23: 3.5
- Suggested problems: pp 207-208: 2, 6, 10, 11, 16
- Hand in Oct 9: p 207: 12 with middle 2 in A changed to 3.
Lecture 15: Fri Sept 25: 3.5
- Suggested problems: p 208: 20, 38, 48, 50
- Hand in Oct 9: p 208: 18
Mon Sept 28: Review
Wed Sept 30: Exam on sections 1.1-3.4.
Lecture 16: Fri Oct 2: 3.6
- Suggested problems: pp 222: 8, 10, 20
- Hand in Oct 9: p 222: 24.
Lecture 17: Wed Oct 7: 3.7 (Markov)
- Suggested problems: p 244: 6, 8, 9
- Hand in Oct 16: p 244: 10. In (c), just do two generations. In (d), guess and verify.
Lecture 18: Fri Oct 9: 3.7 (Population growth)
- Suggested problems: pp 245-246: 20, 24. Remember that L keeps track of females.
- Hand in Oct 16: p 245: 22. Hint: What happens after three generations?
Lecture 19: Mon Oct 12: 4.1
- Suggested problems: pp 259-260: 6, 12, 14, 20.
- Hand in Oct 16: p 261: 26 with 2 replaced by -4
Lecture 20: Wed Oct 14: 4.2
- Suggested problems: pp 280-281: 2, 14, 16, 22
- Hand in Oct 23: p 280: 8
Lecture 21: Fri Oct 16: 4.2
- Suggested problems: p 281-282: 34, 40, 50, 60
- Hand in Oct 23: p 282: 58 with 2 replaced by a variable A, which can represent any number
Lecture 22: Mon Oct 19: 4.3
- Suggested problems: pp 295-296: 4, 6, 12, 16
- Hand in Oct 23: p 295: 8
Lecture 23: Wed Oct 21: 4.4
- Suggested problems: pp 306-307: 4, 6, 8
- Hand in Oct 30: p 307: 11 (Show your work)
Lecture 24: Fri Oct 23: 4.4
- Suggested problems: p 307: 16, 20, 24
- Hand in Oct 30: p 307: 23. Show your work. You need not multiply out three matrices at the end.
Lecture 25: Mon Oct 26: 4.5
- Suggested problems: p 320: 6, 10 (Use k=5)
- Hand in Oct 30: p 320: 22
Lecture 26: Wed Oct 28: 4.6 (Markov) pp 322-326
- Suggested problems: p 356: 4, 7
- Hand in Nov 13: p 356: 8
Lecture 27: Fri Oct 30: 4.6 (Population growth) pp 327-329
- Suggested problems: p 356: 14 (Hint: eigenvalue is an integer), 20 (Use calculator to find root of characteristic polynomial)
- Hand in Nov 13: p 356: #19 with 3 changed to 2
Lecture 28: Mon Nov 2: Handout on Genetics
- Suggested problem: #1 from genetics handout
- Hand in Nov 13: #1 from genetics handout modified so that AA is always fertilized with Aa, Aa with aa, and aa with AA.
Wed Nov 4: Review
Fri Nov 6: Exam on Sections 3.5-4.5
Lecture 29: Mon Nov 9: Handout on Genetics
- Hand in Nov 13: Fertilize with Aa, then with its own genotype, then repeat, fertilizing again with Aa, itself, etc. a. Write the transition matrix for a 2-generation transition and find its eigenvalues. (b). For the eigenvalue with largest absolute value, 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 11: Matrix of Linear Transformation, Handout. (available under Course Documents).
- Suggested problems: see handout
- Hand in Nov 20: see handout
Lecture 31: Fri Nov 13: 5.1
- Suggested problems: pp 373-374: 6, 10, 14, 20
- Hand in Nov 20: p 429: 6
Lecture 32: Mon Nov 16: 5.2
- Suggested problems: p 384: 6, 8, 18
- Hand in Nov 20: p 384: 12
Lecture 33: Wed Nov 18: 5.3
- Suggested problems: p 392: 6, 10, 16, 18
- Hand in Dec 4: p 392: 12
Lecture 34: Fri Nov 20: 5.4
- Suggested problems: pp 404-405: 2, 6, 20, 22
- Hand in Dec 4: p 405: 24
Lecture 35: Mon Nov 23: 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 4: p 595: 11 (Also, graph the points and the line.)
Lecture 36: Mon Nov 30: 7.3
- Suggested problem: p. 596: 16 (Change last point to (4,0). Also, compare values on curve with data points.)
- Hand in Dec 4: p 596: 26 with the 7 changed to a 2. (Also, compare values.)
Lecture 37: Wed Dec 2: Google algorithm, handout
Fri Dec 4: Review