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General Information Syllabus Homework Assignments Classroom Demos
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Weekly Homework Assignments

Sept 20 - 24, 1999 Sept 27 - Oct 1, 1999 Oct 4 - 8, 1999 Oct 11 - 15, 1999
Oct 18 - 22, 1999 Oct 25 - 29, 1999 Nov 1 - 5, 1999 Nov 8 - 12, 1999
Nov 15 - 19, 1999 Nov 22 - 26, 1999 Nov 29 - Dec 1, 1999  


Greetings (3.145.93.221) !

Final Exam has been scheduled: Sunday, December 5, 4 - 6pm, Spaulding Auditorium

Q & A for the Final Exam has been scheduled: Friday, December 3, 4 - 6pm, 101 Bradley


3 Nov: Thanksgiving Schedule: The syllabus seems to be well in hand, and both sections of Math 8 met during xhours during the week of Harvard Weekend, so there will be class on Monday, November 22, but then no class until Monday, November 29. In particular, no class on November 23 or 24.


Week of Nov 15 - End of Term
Assignments Made on:
Monday (due Wednesday): (Assignment 24)
  • Study: Chapter 12.7
  • Do: pp. 749 - 750: 1, 3, 5, 11, 13, 21
Wednesday (due Friday): (Assignment 25)
  • Study: Chapters 12.7
  • Do: pp. 749 - 750: 7, 9, 14, 17, 23, 26
Friday (due Monday): (Assignment 26)
  • Study: Chapter 13.1
  • Do: p 778: 1, 3, 5, 7, 9, 11, 17
Monday 11/22 (due Monday 11/29): (Assignment 27)
  • Study: Chapter 13.2
  • Do: p. 785: 1, 3, 5, 7, 9
Monday 11/29 (due Wednesday): (Assignment 28)
  • Study: Chapters 13.3
  • Do: p. 793: 1, 3, 5, 9, 11, 13


Week of Nov 8 - Nov 12, 1999
Second Hour Exam Monday, November 8: Details below.
Assignments Made on:
Monday (due Wednesday): (Assignment 21)
  • Study: Chapter 12.3 and 12.4
  • Do: p 714: 3, 5, 7, 11, 25
    p. 719: 3, 5, 6
Wednesday (due Friday): (Assignment 22)
  • Study: Chapters 12.3 and 12.4
  • Do: p 714: 13, 15, 17, 23
    p 719: 7, 9, 17, 18
Friday (due Monday): (Assignment 23)
  • Study: Chapter 12.5
  • Do: p 730: 1, 3, 7, 9, 11, 13


Week of Nov 1 - Nov 5, 1999
Second Hour Exam Monday, November 8: Details below.
Assignments Made on:
Monday (due Wednesday): (Assignment 18)
  • Study: Chapter 10.6 and class notes
  • Do: HTML    PDF    PS    DVI    TeX
Wednesday (due Friday): (Assignment 19)
  • Study: Chapters 10.6 and class notes
  • Do: HTML    PDF    PS    DVI    TeX
Friday (due Monday): (Assignment 20)
  • Study: Chapter 12.1, 12.2
  • Do: p. 701: 1, 3, 5, 12, 14, 19, 20, 28
    p 706: 1, 3, 5
Second Hour Exam Information

The second Math 8 exam will be held Monday, November 8 from 4 - 6 pm. Arkowitz's section will be in Cook Auditorium (Murdough Center); Shemanske's will be in Filene Auditorium (Moore Hall). The exams for both sections are identical, but seating in Filene is limited. Please go to the room according to the section in which you are registered. If in doubt, check the official list.

Note: Those people (and only those people) with labs or other classes whose normal class times overlap with our scheduled exam period, may take the Math 8 exam from 7 - 9 pm in Silsby 123 (on the same day). You should arrive promptly. Please notify your instructor if you are in this situation.

Finally, if you will be away for a College-sponsored activity, you should speak to your instructor to see if you can arrange to take the exam prior to your departure. There are no makeup exams.

The exam covers all material from Assignment 10 through Assignment 18.

The exam is designed so that well-prepared students can complete the exam in one hour, however you will be given two hours for the exam which should eliminate time pressure considerations for all students.

Please arrive by 3:45 pm to allow ample time to get seated, settled, and exams distributed by 4:00. Since seating in Filene is limited, please take seats leaving exactly one empty seat between you and your neighbor(s). Seating in Cook is more flexible, but there should be at least one empty seat between you and your neighbor(s).

Naturally, bring writing implements; pens or (sharpened) pencils are fine. Scrap paper will be attached to each exam; you may not use your own.

Calculators may be used for numerical work or graphing if you like, but under no circumstances are they to be used in any other way, e.g., to store information, run programs, symbolic manipulation. They are certainly not required, nor should they be of much use. Except in trivial cases or when requested, answers need not be simplified and more importantly, answers need to be exact. For example, someone saying the answer to a problem is 1.414213562 instead of the correct answer of sqrt(2) is wrong, and will lose credit accordingly.

There will be a Question and Answer session on Sunday (November 7), starting at 7pm in Filene Auditorium (Moore Hall).

Sample questions will be available via the Math 8 home page by the end of the week.


Week of Oct 25 - Oct 29, 1999
Assignments Made on:
Monday (due Wednesday): (Assignment 15)
  • Study: Chapter 10.4 and class notes
  • Do: HTML    PDF    PS    DVI    TeX
Wednesday (due Friday): (Assignment 16)
  • Study: Chapters 10.4 and class notes
  • Do: p. 631: 2, 4, 5, 7, 8, 25 and
    Find the angle between the planes 2x - 3y - 4z = 8 and 3x + 2y - z = 4
Friday (due Monday): (Assignment 17)
  • Study: Chapter 10.6 and class notes
  • Do: HTML    PDF    PS    DVI    TeX


Week of Oct 18 - Oct 22, 1999
First Hour Exam Monday October 18: Details below.
Assignments Made on:
Monday (due Wednesday): (Assignment 12)
  • Study: Chapter 10.1, 10.2
  • Do: p. 603: 1, 3, 5, 15, 19
Wednesday (due Friday): (Assignment 13)
  • Study: Chapters 10.2
  • Do: p. 613: 2, 3, 10
Friday (due Monday): (Assignment 14)
  • Study: Chapter 10.3
  • Do: p. 622: 1 - 6


Week of Oct 11 - Oct 15, 1999
First Hour Exam Monday October 18: Details below.
Assignments Made on:
Monday (due Wednesday): (Assignment 9)
  • Study: Chapter 4.8
  • Do: p. 287: 1, 3, 5, 7, 9, 11, 13
Wednesday (due Friday): (Assignment 10)
  • Study: Chapters 9.5, 9.8
  • Do: p. 564: 1, 3, 4, 5 [No interval of convergence], plus the problem below:

    • Determine what degree Taylor polynomial is required to guarantee an error of less than 10^(-14) for sin(x) on the interval [-pi, pi].
Friday (due Monday): (Assignment 11)
  • Study: Chapter 9.2, 9.6
  • Do: p. 533: 1, 2, 5, 7 and p. 573: 1, 5, 7
First Hour Exam Information

The first Math 8 exam will be held Monday, October 18 from 4 - 6 pm. Arkowitz's section will be in Cook Auditorium (Murdough Center); Shemanske's will be in Filene Auditorium (Moore Hall). The exams for both sections are identical, but seating in Filene is limited. Please go to the room according to the section in which you are registered. If in doubt, check the official list.

Note: Those people (and only those people) with labs or other classes whose normal class times overlap with our scheduled exam period, may take the Math 8 exam from 7 - 9 pm in Silsby 123 (on the same day). You should arrive promptly. Please notify your instructor if you are in this situation.

Finally, if you will be away for a College-sponsored activity, you should speak to your instructor to see if you can arrange to take the exam prior to your departure. There are no makeup exams.

The exam covers all material from the beginning of term through Assignment 9.

The exam is designed so that well-prepared students can complete the exam in one hour, however you will be given two hours for the exam which should eliminate time pressure considerations for all students.

Please arrive by 3:45 pm to allow ample time to get seated, settled, and exams distributed by 4:00. Since seating in Filene is limited, please take seats leaving exactly one empty seat between you and your neighbor(s). Seating in Cook is more flexible, but there should be at least one empty seat between you and your neighbor(s).

Naturally, bring writing implements; pens or (sharpened) pencils are fine. Scrap paper will be attached to each exam; you may not use your own.

Calculators may be used for numerical work or graphing if you like, but under no circumstances are they to be used in any other way, e.g., to store information, run programs, symbolic manipulation. They are certainly not required, nor should they be of much use. Except in trivial cases or when requested, answers need not be simplified and more importantly, answers need to be exact. For example, someone saying the answer to a problem is 1.414213562 instead of the correct answer of sqrt(2) is wrong, and will lose credit accordingly.

There will be a Question and Answer session on Sunday (October 17), starting at 7pm in Filene Auditorium (Moore Hall).

Sample questions will be available via the Math 8 home page by the end of the week.


Week of Oct 4 - Oct 8, 1999
Assignments Made on:
Monday (due Wednesday): (Assignment 6)
  • Study: Chapter 17.7 (Ignore Euler equations and complex roots)
  • Do: p. 1015: 1, 3, 5, 14, 19, plus the two problems below:

    • Find the general solution to the differential equation (D^2 -4)(D -2)y = 0
    • Verify that 2x+3 is a solution to the differential equation y'' - 3y' + 2y = 4x, and use this information to find the general solution to this differential equation.
Wednesday (due Friday): (Assignment 7)
  • Study: Chapters 17.7 (complex roots), Appendix I
  • Do: p. 1015: 7, 9, 15, 21 plus the problems below:

    1. Write (2 + 3i) / (1 - 5i) in the form a + bi
    2. Compute the complex conjugate and modulus of 3 + 4i
    3. Write -1 + sqrt(3)*i in polar form
    4. Simplify (1 + i)20 (Use polar form)
Friday (due Monday): (Assignment 8)
  • Study: Chapter 7.1
  • Do: p. 415: 5, 6, 8, 13, 21

    • Hint for 21: First suppose the the region is also bounded by x = b for some b > 0. Compute the volume of this region, and take the limit as b --> infinity.


Week of Sept 27 - Oct 1, 1999
Assignments Made on:
Monday (due Wednesday): (Assignment 3)
  • Study: Chapter 6.1
  • Do: p. 351: 1, 5, 6, 9, 13, 17, 22, 34
Wednesday (due Friday): (Assignment 4)
  • Study: Chapters 7.9, 17.4
  • Do: p. 994: 1, 6, 7, 9, 11 (For 11, solve both as a separable and first order linear differential equation), plus the problem below:

    • Into a 2000 liter container is placed 1000 liters of a brine solution containing 40 kg of salt. A brine solution containing .02 kg/l of salt flows into the container at a rate of 50 l/min. The solution is kept thoroughly mixed, and the mixture flows out at a rate of 25 l/min. How much salt is in the container at the moment it overflows?
Friday (due Monday): (Assignment 5)
  • Study: Chapters 3.7(skim), 17.1
  • Do: pp. 983 - 984: 1, 3, 5, 7, 11, 13, plus the problem below:
    • Find the general solution to the differential equation (D-1)(D-2) y = x by solving the system of first order linear differential equations:
      1. (D - 2)y = u
      2. (D - 1)u = x (solve me first!)


Week of Sept 20 - 24, 1999
Assignments Made on:
Monday: No class
Wednesday (due Friday): (Assignment 1)
  • Review: Chapters 1 - 5 (as required)
  • Skim: Chapter 17, sections 1 and 5

    • Do: the problems on the homework supplement distributed in class.
    (If you didn't pick up a copy in class, you can download this copy to your hard disk, and drag it onto your desktop printer icon. If you are printing to a postscript printer (e.g. a Kiewit printer), choose the postscript version, otherwise choose the pdf version. The pdf version will probably print in all cases, and is viewable via Acrobat Reader. There are notes about handling pdf files in the Maple notes which you are to read below.)
  • Finally:
    1. Explore the Math 8 web pages, and make a bookmark for future reference. Among other things, here you will find all of the general information about the course, including information about exams, tutorials, and grades.
    2. Also check out the Homework Assignments page. That's this page! Future assignments will be posted to the web site, and will not be handed out in class, so if you have problems with Netscape, let your instructor know. Even better, try the comments/questions page to see if somebody else in the class can help!
    3. Navigate to the Information for using Maple page. Carefully read this page and follow the instructions for downloading a keyserved version of Maple, and obtaining a short Maple primer.
Friday (due Monday): (Assignment 2)
  • Study: Chapter 3, section 4 and Chapter 17, section 2
    [separable only, no homogeneous]
  • Do: p. 988: 1, 5, 8, 13, 14, 21
    p. 200: 11, 17, 23 plus the two problems below:

    1. A tank contains 1000 liters of brine with 15 kg of dissolved salt. Pure water enters the tank at a rate of 10 liters/min. The solution is kept thoroughly mixed and drains from the tank at the same rate. How much salt is in the tank
      (a) after t minutes? (b) after 20 minutes?
    2. A tank contains 1000 liters of pure water. Brine that contains 0.05 kg of salt per liter of water enters the tank at a rate of 5 liters/min. Brine that contains 0.04 kg of salt per liter of water enters the tank at the rate of 10 liters/min. The solution is kept thoroughly mixed and drains from the tank at 15 liters/min. How much salt is left in the tank
      (a)after t minutes? (b)after 1 hour?



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