## Weekly Syllabus and Assignments

### Week of Sept 22 - 26, 1997

• Monday: No class
• Wednesday: (Assignment 1)
• Review: Chapters 1, 2, 3, 4, 5, 7(as required)
• Study: Chapter 17, section 1

• Do: the problems on the homework supplement.
• Finally:
1. Use Netscape to find the Math 11 home page, and make a bookmark for future reference. Here you will find all of the general information about the course, including information about exams, tutorials, and grades.
2. Once there, navigate to the weekly syllabus and 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.

• Friday: (Assignment 2)
• Study: Chapter 17, sections 2 and 4

• Do: p. 1231: 1 -- 5
p. 1249: 3, 10, 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?

### Week of Sept 29 - October 3, 1997

• Monday: (Assignment 3)
• Study: Chapter 8, section 1
• Do pp. 583 - 584:  1, 7, 13, 20, 21, 24, 28, 51a
• Wednesday: (Assignment 4)
• Study: Chapter 8, section 2
• Do pp 591 - 592: 1, 3, 5, 9, 10, 11, 14, 33
• Friday: (Assignment 5)
• Study Chapter 8, section 3 (don't worry about hyperbolic functions)
• Do page 601:  1, 3, 5, 10, 13, 17, 31, 34

### Week of October 6 - October 10, 1997

• Monday:  (Assignment 6)
• Study:  Chapter 8, section 4
• Do page 611:  7, 9, 11, 13, 17, 24
• Wednesday:  (Assignment 7)
• Study:  Chapter 17, section 3 (no exact equations)
• Do page 1239:  7 - 12 and 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:  (Assignment 8)
• Study:  Chapter 17, section 5 and skim section 7
• Do page 1258:  1, 3, 9, 11, 13, 17, 19

### Week of October 13 - October 17, 1997

#### First Hour Exam Next Wednesday: Details here soon

• Monday:  (Assignment 9)
• Study:  Chapter 17, section 5 and class notes on complex numbers
• Do pp 1258 - 1259:  5, 7, 15, 21, 23
• Also do the following problems:
• Write (2 + 3i) / (1 - 5i) in the form a + bi
• Compute the complex conjugate and modulus of 3 + 4i
• Write -1 + sqrt(3)*i in polar form
• Simplify (1 + i)^20  (Use polar form)
• Find all solutions in the complex numbers to the equation z^5 = 32
• Wednesday:  (Assignment 10)
• Study Chapter 6, sections 1 and first part of section 2
• Do pp 397 - 398:  12, 13
• Do page 409:  8, 9
• Do page 611:  27a
• Do page 601:  29
• Find the area bounded by the curves y = x^3 - 3x and y=x.
• Friday:  (Assignment 11)
• Study Chapter 6, sections 2 and 3
• Do pp 409 - 410:  11, 15, 33
• Do page 419:  17, 19, 21
• Do page 584:  32

### Week of October 20 - October 24, 1997

• Monday:  (Assignment 12)
• Study Chapter 8, section 6 (first part)
• Do pp 635 - 636:  1, 5, 9, 11, 49, 51, 53
•  Tuesday :  Optional Question and Answer Period
• Arkowitz:  107 Steele, 7pm
• Shemanske:  3 Rockefeller, 7pm
• Wednesday:  (Assignment 13)
• Study Chapter 8, section 6 (second part)
• Do pp 635 - 637:  23, 27, 31, 43, 62, plus (in Maple notation):  Determine whether the following integrals converge or diverge.
• int(1/(x^3 - 5), x = 2..infinity)
• int(1/(sqrt(x) + x^2), x=0..1)
• int(1/(sqrt(x) + x^2),x=1..infinity)

First Hour Exam Information

The first Math 11 exam will be held Wednesday, October 22 from 5:30 - 7:30pm in Cook Auditorium.

• The exam covers all material from the beginning of term through Assignment 10.
• 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 5:15 to allow ample time to get seated, settled, and exams distributed by 5:30.  The room will be crowded since both sections of math 11 will be present.  To make life easier, please sit with precisely one empty seat between you and your neighbor.
• 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, 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 two Question and Answer sessions on Tuesday (October 21), starting at 7pm.  Arkowitz's Q &A will be in 107 Steele, and Shemanske's will be in 3 Rockefeller.

• Friday:  (Assignment 14)
• Study:  Chapter 5, section 5 (No error estimates until Monday)
• Do pp 377 - 378:  1, 5
• pp 637 - 638:  78a, 79a, 82, 84a
• Finally using the functional equation for the Gamma function defined in class [Gamma(z+1) = z*Gamma(z)], and the fact that Gamma(1/2) = sqrt(Pi), compute Gamma(3/2), and Gamma(5/2).

### Week of October 27 - October 31, 1997

• Monday:  (Assignment 15)  (HW due before Wednesday's class)
• Study:  Chapter 5, section 5 (Error estimates), skim the beginning of Chapter 10, section 1
• Do page 378:  7, 9, 11, 16, and continue with #16 by computing a value of n so that the approximation of the integral in 16 using Simpson's rule (with n subintervals) has an error < 5 x 10^(-8).
• Tuesday:  (Assignment 16) (HW due by 11:15 am on Friday)
• Study:  Chapter 10, section 1 (no remainders or error estimates)
• Do page 734:  1, 3, 7, 9, 11
• Wednesday:  (Assignment 17) (HW due before Monday's class)
• Study:  Chapter 10, section 2
• Do page 752:  1a, 3a, 5, 7, 9, 17, 19, 30, 35, 41, 46

### Week of November 3 - November 7, 1997

Remember:  The second hour exam is next week Wednesday, November 12 at 5:30pm, and covers assignments 11 through 19.

• Monday:  (Assignment 18)
• Study:  Chapter 10, section 3
• Do pp 767 - 769:  11, 13, 21, 25, 31, 35, 37, 42
• Wednesday:  (Assignment 19)
• Study:  Chapter 10, section 4
• Do pp 776 - 777:  3, 11, 19, 21, 29, 31, 34, 47
• Friday:  (Assignment 20)
• Study:  Chapter 10, section 5
• Do pp 780 - 781:  1, 3, 5, 7, 10, 12, 17, 24

### Week of November 10 - November 14, 1997

• Monday:  (Assignment 21)
• Study:  Chapter 10, section 6
• Do pp 787 - 789:  6, 11, 13, 21, 23, 25, 29, 31

•  Tuesday :  Optional Question and Answer Period
• Arkowitz:  107 Steele, 7pm
• Shemanske:  3 Rockefeller, 7pm
• Wednesday:  (Assignment 22)  Second hour exam today
• Study:  Chapter 10, section 7
• Do pp 793 - 794:  5, 7, 9, 11, 17, 25, 27, 31
The exam covers assignments 11 (volumes by shells) - 19 (Integral and Comparison tests).  The exam will again be in Cook Auditorium from 5:30 - 7:30pm.  Please arrive by 5:15, and sit in alternate seats to accommodate the crowd.
• Friday:  (Assignment 23)
• Study:  Chapter 10, section 8
• Do pp 800 - 801:  3, 5, 14, 19, 25, 27, 31

### Week of November 17 - November 21, 1997

• Monday:  (Assignment 24)
• Study:  Chapter 10, section 9
• Do page 812:  1, 7, 10, 13, 21, plus the following problem:
• You have just been hired by Texas Instruments to help build a new calculator.  Your job is to create the sine and cosine algorithms, and your mission is to able to approximate the value of sine and cosine for any number a user enters with an error of < 10^(-14).  Fortunately, you still have your class notes from Math 11 in which you learned how to use Taylor polynomials to approximate both of these functions.
• First, give an argument which convinces a learned reader that you really need only be able to approximate the values of sine and cosine for x in [-pi/4, pi/4], given that your algorithm can also include various trigonometric identities and properties. For example, explain how the property sin(x) = sin(x + 2*pi), allows you to simplify your task of allowing for any number to be entered by the user, to simply knowing the values of sine and cosine for x in [-pi,pi].  Now continue on your own.  After all, that's why TI is paying you the big bucks.
• Next determine what degree Taylor polynomial is required to guarantee an error of less than 10^(-14) for sin(x) on the interval [-pi/4, pi/4].
• Wednesday:  (Assignment 25)
• Study Chapter 11, sections 1 and 3 (first part of 3)
• Do page 836:  9, 13, 21, 33
• Do page 851:  2b, 3e, 9a,d
• Friday:  (Assignment 26)
• Study:  Chapter 11, sections 2 and 3
• Do pp 844 - 845:  9, 16, 31
• Do pp 851 - 852:  11, 12, 25, 34

### Week of November 24 - November 28, 1997

#### Classes meet Monday at the regular time and Tuesday during the xhour.  There will be no class on Wednesday.

• Monday:  (Assignment 27) (Due by Wednesday, class time)
• Study:  Chapter 11, section 4
• Do pp 862 - 863:  1, 9, 15, 16, 19, 21, 27, plus what is the significance of the different answers in 15, 16?
• Tuesday:  (Assignment 28) (Due before class on Monday, December 1)
• Study:  Chapter 11, section 5
• Do pp 868 - 869:  1, 3, 5, 9, 15, 17, 21, 23
•  Wednesday - Sunday:  (Thanksgiving break)