| Prerequisites:
Mathematics 205 or equivalent. General Description: College level
second semester calculus course wherein the treatment of
differential and integral calculus of functions of one
variable began in Mathematics 205 is completed, sequences
and infinite series are studied, and the exposition of
the analytic geometry of planar curves is concluded.
Emphases: The
following mix of topical emphases is recommended for
instructors in determining the accountability of what the
Mathematics 206 student will be tested and quizzed upon.
- Theoretical/Conceptual
aspects of the material: 15 - 20%
- Geometrical
Interpretations of the material: 10 - 15%
- Algorithmic/Computational
aspects of the material (including computer and
graphics calculator usage): 50%
- Applications of the
material inside and outside of mathematics: 15 -
20%
These aspects are, of
course, not compartment but quite often overlap,
complement, and reinforce one another. The standard
example of a topic in this course viewed from these four
different angles is the derivative. Students should
understand that the derivative is the limit of a
difference quotient and that geometrically it yields the
slope of the tangent line (and the curve) at a given
point on the curve. Students should be able to use the
many basic differentiation rules and notation correctly
and with facility; also they should understand that the
most basic application of the derivative involves
measuring instantaneous rate of change such as the
velocity of a moving object.
Textbooks and
Supplements: (available in the bookstore for
students)
Required:
Calculus by R.L. Finney and G.B.
Thomas, Addison-Wesley 1994/2nd edition
Recommended:
Student's Solutions Manual Part I
by M. Schneider and T. L. Cochran, Addison-Wesley
1994
Student's Study Guide Part I by M. D.
Weir, Addison-Wesley 1994
Exploring Calculus with Maple by
Holmes/Ecker/Boyce/Siegmann, Addison-Wesley, 1993
edition
Exploring Calculus with Derive by D. C.
Arney, Addison-Wesley, 1992
Resources available
as desk copies from Betty:
Student's Study Guide Part I
Student's Solutions Manual Part I
Instructor's Solutions Manual Part I
Calculus Explorer Software for the PC
Printed Test Bank
Transparency Masters
Please tell your students
to buy only Part I of the Student's Study Guide at this
time. It augments Chapters 1-12 (our Mathematics 205-206)
of Calculus. Volume 2 covers topics in Chapter 9-15, some
overlap plus multivariable calculus (our Mathematics
301).
Maple in Mathematics
206 Maple now is a required component in Mathematics
206. Every class will have one extra lab hour on Maple
every week. A minimal set of Maple commands compiled by
Thomas to be covered in Mathematics 205 is used as a
common reference guide for all Mathematics 206 classes.
While it is up to the instructor to do more, this set of
commands will assume a common ground for Mathematics 206
instructors.
The department will assign
GTA to every Maple lab. Please be aware of that a GTA may
serve under several instructors. In general, we
instructors are expected to conduct or, at least, be
present in our Maple labs. It is up to the instructor how
to run the lab and how to integrate it into the class.
Typically, the instructor will demonstrate the commands,
functions, and calculations in the standard classroom
setting. The students will practice using the system on
various exercises, assignments or projects during lab
hour. From past experience of our faculty, four to five
projects may be adequate for one semester. This would
give a time interval of three or four weeks between two
projects. Not all students have had adequate experiences
on computers. It may take a while for some of them just
to get the mouse pointing at the right spot on the
screen.
We may need to remind our
students from time to time that we use technologies to
enhance our learning and problem solving abilities.
Without a good understanding of the subject and methods
behind the screen, we may not be able to apply a
technology efficiently, meaningfully or correctly. If you
don’t allow your students to use Maple on at least a
considerable part of the final exam, please tell them in
your syllabus. We would recommend that no computer usage
in the final exam.
Several faculties have
been using Maple in their calculus classes, and have
developed projects and assignments on Maple. I listed
here some available material. You may get a copy either
from me or from them directly. If you would like to share
your projects in the future, please let me know.
Books about Maple
You may require your
student to buy a book for the Maple lab if you
prefer. Please let Betty know if you do so. The
following are some know books available.
Discovering
Calculus with MAPLE by Kent Harris and
Robert Lopez, Second Edition, Wiley ISBN:
0-471-00973-3
Exploring
Calculus with Maple by
Holmes/Ecker/Boyce/Siegmann, Addison-Wesley,
1993.
Handouts, Projects
and Worksheets developed by Faculties
- An
introduction to Maple for Math 205.
Thomas Riedel.
This is the minimal list of commands we
adopted. It is available in Maple worksheets
from Thomas or me. (I will put it on Merlin
in the future so that you can access it from
Maple directly.) This document was prepared
for the instructors as well as students. It
also intends to help those Mathematics 206
students who took Mathematics 205 in the
"old system".
- Maple
Worksheets, George Barnes and
Inessa Levi.
This is a large collection of Maple
worksheets with many examples from every
section of the textbook. George and Inessa
used it in their regular class lectures in
the past. It is available on Merlin in the
directory sys/course/mathematix/math/levi/205. You can open any
section of it directly from Maple in the lab.
Hard copy is also available.
- Maple Labs
for Calculus, André Kézdy.
It contains several Maple projects André
used in his class. You may ask him for an
updated version from Kézdy in the future.
- Maple
Worksheets, etc. Willy W. Williams.
There are some developing worksheets used in
previous class, as well as some materials
collected from the web. You can access them
on Merlin in sys/course/mathematix/math/Williams/205
and sys/course/mathematix/math/Willimas/Mapleres.
Software
- Online
Math Generator, Chi Wang. This is
designed for student practice exercise within
Maple. Some selected topics from Calculus are
available. One can access it from the web in
our lab or at home. Exercises are generated
inside Maple with expandable link for
explanation and exploration. Each time one
gets a different set of problem. Mathematics,
text and Maple commands are automatically
generated. Student can use it without know
about Maple syntax. the web address is http://www.louisville.edu/~c0wang01/maple.
Other
resources on the web
Links to various
resources on the web can be found in our department
home page at http://www.louisville.edu/groups/math-www/mathlinks.html.
Get a copy of
Maple
Maple is available in
the Mathematics Computer Lab. Please advise the
students that they can purchase a copy of Maple
through IT for only $15, which is an excellent deal
that beats any type of calculator available on the
market.
Calculator Policy:
We recommend that, as a general rule, Mathematics 205-301
students should be allowed to use any type of calculator
(scientific, graphical, programmable) they care to employ
on homework, projects, quizzes and tests. It is certainly
appropriate to ban the use of the more sophisticated
calculators on specific questions on a given test (e.g.,
when testing students' conceptual knowledge of using the
chain rule or doing integration by substitution). At the
college level, we should follow the calculator/computer
usage guidelines embodied in the new NCTM Standards for
students in grades K-12. Students should be allowed to
use all available technology after mastering the
conceptual aspects of a given mathematics topic.
Computer Usage in
Mathematics 206:
Maple will be a required
component in Mathematics 205 during this Fall. Every
class will have one extra lab hour on Maple every week.
It will be in Mathematics 206 from Spring. A minimum set
of Maple commands to be covered in Mathematics 205 is
incorporated in a short document. Those commands will be
the foundation for Mathematics 206 instructors in the
future. At mean time, Maple, Derive, Math-CAD and Visual
Calculus are available in the University Computer Center.
Maple is available in the Mathematics Computer Lab.
Please advise your student that they can purchase a copy
of Maple through IT for only $15, which is an excellent
deal that beats any type of calculator available on the
market. Mathematica is also available on homer. Student
can access it from both graphic and nongraphic terminals.
Final Exam: During
this Fall semester all sections of Mathematics 206,
except one, will be taught by regular faculties. I will
recommend to the department not to give combined final
exam. You will be informed on this matter as soon as
possible.
Other Available
Material from coordinator: Old tests, sample finals,
syllabi, and advice.
Paced Syllabus
Each day section of
Mathematics 205 meets three days per week for 75 minutes.
All told there are 42 class meetings and 37 sections to
cover in the text starting from 6.6 and finishing at
10.8. In average, you need to cover more than one section
per. Some of the modeling in 7.5 through 7.8 can be
combined. Numerical integration was done in Mathematics
205, but little was done on area between curves. The
following paced syllabus is written to reflect the
situation just detailed. It allows for four full-period
tests and little time for repetition and review.
| Week |
Section/Tests |
Comments |
| 1 |
6.2, 6.6 - 6.8 |
6.2 reviews inverse functions and
their derivatives, and should be done before 6.8. |
| 2 |
6.9 - 6.11 |
This is a two-lecture week due to
the Martin Luther King Day. Do not spend too much
time on 6.11 hyperbolic functions. |
| 3 |
7.1 - 7.3 |
Review some of 5.3. Little area
calculations were done in Mathematics 205. |
| 4 |
7.4, Test 1, 7.5 |
Work is the main application
covered. |
| 5 |
7.6 - 7.8, 8.1 |
Pick some of the applications from
7.6, 7.7. |
| 6 |
8.1 - 8.3 |
Review substitution with 8.1. Enough
exercises will help students to pick up what was
taught in Mathematics 205 again. Most mistakes
students made in this chapter are on formulas
learned in Math 205. Integration by parts is most
important here. Partial fractions can be done by
computer but the concept is important. |
| 7 |
8.4 - 8.6 |
In the spirit of the "Lean and
Lively Calculus" and given the ubiquity of
calculus software and graphical calculators, the
students should be held responsible only for
straightforward integrals involving trigonometric
substitution and partial fractions. |
| 8 |
Test 2, 9.1 |
|
| 9 |
9.2 - 9.4 |
Sequence and infinite series are
quite difficult for most of our students, review S - notation. |
| 10 |
Spring
Break |
|
| 11 |
9.5 - 9.7 |
Begin with in 9.3, 9.4 are tests for
nonnegative series. Emphasize comparison with
geometric series. |
| 12 |
9.8 - 10.1 |
|
| 13 |
Test 3, 10.2, 10.3 |
10.1 and 10.2 can be condensed to
leave more time for parametrizations of curves
and polar coordinates. |
| 14 |
10.4 - 10.6 |
Give enough time for 10.5. |
| 15 |
10.7, 10.8, Test 4. |
Polar coordinates, graphs and
equations are important for Mathematics 301. |
| 15 |
Review |
Only one day this week. |
Homework
Selections: The following homework assignment is for
your reference.
| Section |
Fundamental |
Practice |
| |
|
|
| 6.2 |
3,5,7,11,15,17,21,25,27,31 |
9,12,19,23,29,35,37,39,43 |
| 6.6 |
5,7,13,19,21,25,29,31,33,37,
39,45,46,55, |
9,11,12,18,35,37,59,61 |
| 6.7 |
1,3,5,11,12 |
7,9,14,16,25 |
| 6.8 |
Odd 1-19,23,27,29,31,37,41,43 |
18,20,35,36,51,55-58 |
| 6.9 |
3,5,13,17,20,23,27,29,31,33,
45,47,53,55,61,69 |
7,11,31,41,48,53,55,71,79 |
| 6.10 |
7,9,15,21,25,35,41,45,55,
57,61,63,65 |
3,5,29,47,51,69 |
| 6.11 |
1,3,5,11,15,17,25,27 |
13,21,31,35 |
| |
|
|
| 7.1 |
1,3,5,7,11,13,15,19,29,37,38 |
2,8,9,23,39,42,47 |
| 7.2 |
Odd 1-11,15,17,23,25,37,41,47 |
19,27,31,35,43 |
| 7.3 |
Odd 1-11,17,23,27,29,35 |
21,29,35,39 |
| 7.4 |
Odd 1-5,7,9,15,25,33,35 |
13,1721,31,42,43,49 |
| 7.5 |
3,5,9,11,13,16 |
15,16,21 |
| 7.6 |
3,5,7 |
9,15,17 |
| 7.7 |
5,11,19 |
7,21,23 |
| 7.8 |
1,3,5 |
9,10 |
| |
|
|
| 8.1 |
odd 1-31, 33,35,39,43,45,51,
55,57,59,61 |
Even 2-32,41,47,53,67,71,79 |
| 8.2 |
1,2,3,5,9,13,15,17,21,31,37 |
7,15,16,17,21,27 |
| 8.3 |
1,3,5,11,15,31,37,39,43 |
7,17,34,40,41,45 |
| 8.4 |
3,7,11,13,23,29,33 |
8,12,20,31 |
| 8.5 |
Odd 1-21,23,39,41,45,59,59,71 |
2,10,31,39,63,83 |
| 8.6 |
Odd 1-9,17,25,39,41,43 |
2,21,31,55,63,71 |
| |
|
|
| 9.1 |
5,7,9,11,13,19,21,23,29,
39,45,46,53,57,61,65 |
32-34,46,55,58,66,71 |
| 9.2 |
1,2,3,5,7,11,15,19,21,23,
25,29,33,35,37,39,45 |
13,17,41,43,51,55 |
| 9.3 |
2,3,5,7,9,11,13,15,19,27,
29,35,37,43,49, |
8,12,18,31,34,39,41 |
| 9.4 |
1,3,5,7,9,15,21,29,31,35,39 |
11,27,41,43 |
| 9.5 |
1,5,13,19,27,33,39,43,46 |
15,16,17,18,26,49 |
| 9.6 |
1,3,5,11,13,22,33,37,41 |
7,27,35 |
| 9.7 |
1,3,5,9,11,17,19,23,27,41 |
4,10,21,25,37,43 |
| 9.8 |
1,11,15 |
7,17,23 |
| |
|
|
| 10.1 |
1-8,9,13,19,25,53,57,61,65,67 |
36,58,63,69,72 |
| 10.2 |
3,5,7,9,17,21 |
4,18,21,25,27,29 |
| 10.3 |
1,5,7,9,15,19,25 |
4,8,17,26,29,31,33,35,37 |
| 10.4 |
3,5,9,13,17,18,23 |
15,21,27,29,35,37 |
| 10.5 |
1,3,11,17,23,29,31,43,47,51,57 |
25,39,53,59 |
| 10.6 |
1,3,5,11,13,17,21,25 |
27,29,31,35,41,45 |
| 10.7 |
1,5,9,15,17,25,33 |
11,13,23,41,45 |
| 10.8 |
1,3,5,7,18,25,33 |
11,17,21,23,35 |
|