Math 11  Fall 1997
Weekly Syllabus and Assignments
(Last Modified 15 November, 1997)
 Week of Sept 22  26, 1997
 Week of Sept 29  Oct 3, 1997
 Week of Oct 6  10, 1997
 Week of Oct 13  17, 1997
 Week of Oct 20  24, 1997
 Week of Oct 27  31, 1997
 Week of Nov 3  7, 1997
 Week of Nov 10  14, 1997
 Week of Nov 17  21, 1997
 Week of Nov 24  28, 1997
 Week of Dec 1  5, 1997
Return to Math 11 Home Page
Week of Sept 22  26, 1997
Assignments Made on:
 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:

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.

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.

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: (Assignment 2)

Study: Chapter 17, sections 2 and 4
Do: p. 1231: 1  5
p. 1249: 3, 10, plus
the two problems below:

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?

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
Assignments Made on:
 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
Assignments Made on:
 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
Assignments Made on:

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
Assignments Made on:

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.

Sample questions are available via the Math 11 home page.

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
Assignments Made on:

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.
Assignments Made on:

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
Assignments Made on:

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
Assignments Made on:

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.
Assignments Made on:

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)
Week of December 1  December 3, 1997
Assignments Made on:

Monday: (Assignment 29)

Study: Chapter 11, section 6

Do pp 879  880: 5, 11, 13, 17, 21, 25, 35, 37

Wednesday: (Study, study, study !)
Final Exam is on Sunday, December 7, 4  6
pm, Cook Auditorium