MONTGOMERY COLLEGE
Department of Mathematics
Rockville Campus
Fall 2010
Course Outline:
MA 181, Calculus I
Course Chair:
Ingrid Scott, 240-567-5216, 213A Science East
ingrid.scott@montgomerycollege.edu
Text:
James Stewart, Calculus, Concepts and Contexts, 4th Edition, Brooks/Cole-Cengage
Publishing Company, 2010
The text is available in a hardbound and a less expensive binder-ready [loose-leaf] version in
the Rockville College bookstore. Binder-ready texts cannot be sold back to the bookstore.
The e-book can be purchased online at www.cengagebrain.com/shop/index.html .
Optional:
Calculus, Concepts and Contexts, 4th Ed., Student Solutions Manual containing solutions for
all odd-numbered exercises.
Calculator:
TI 83/83+, 84/84+ preferred. Note: students should not be permitted to use a TI-89, TI-92,
or other equivalent calculators containing computer algebra system capability.
MA 181 is an introduction to the major ideas of single variable calculus. The topics include limits, derivatives,
integrals and applications of algebraic and transcendental functions. The text uses a four-fold approach (analytical,
graphical, numerical and verbal) to problem solving. Applications incorporating problem solving presented in the
context of real world situations with an emphasis on model creation and interpretation should be integrated
throughout the course.
COURSE INFORMATION:
(1)
(2)
TESTS & FINAL EXAM: The course outline allows time for 4 or 5 one-hour tests and reviews in addition to the
required two-hour final examination.
 Take-home or open book exams should be kept to a minimum. There is no way to guarantee that students
do not receive help on take-home exams from other students, tutors, or computer algebra systems. Please
give the Math/Science Center a copy of such tests in advance in order to alert tutors to not assist your
students with the test questions. Take-home quizzes and tests should not count for more than 10  15%
of the final grade.
 Part-time instructors should send one copy of each test, including the grade distribution, to the Course
Chair as soon as possible after the test is given. Any open-book or take-home tests should be so identified.
FORMULAS: The Rockville Mathematics Department instituted a policy regarding the use of formulas,
whether on paper or stored in calculators.
For MA 181, the following definitions and formulas should be tested without the aid of a formula sheet
or calculator at least once during the semester.
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2
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
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

Definitions
Limit definition of continuity at a point
Limit definition of the derivative
Derivatives and Antiderivatives
Derivatives of x n , e x , ln x, sin x, cos x, tan x
The Product rule, Quotient rule, Chain rule, including problems that involve the use of these and the basic
formulas above in combination with one another.
Antiderivatives of x n , e x , sin x,cos x, sec2 x
Students should also be exposed to the following formulas during the semester and should be required to
use some or all of them on quizzes or tests that may allow the use of a formula card or calculator.
(3)
(4)

Derivatives of sec x, cot x, csc x, ln x , a x , log a x, sin 1 x, tan 1 x

Antiderivatives of sec x tan x,
1
1
,
2
1 x
1  x2
CALCULATORS: Instructors should use appropriate technology throughout the course. Since our students are
required to have graphing calculators, students should be encouraged to make use of them in class, when
doing homework, and when taking quizzes and tests other than those subject to the formula policy
restriction discussed in #2 above. Please contact the Math/Science Center, Room 02 Macklin Tower (240567-5200), in order to obtain an overhead graphing calculator for classroom presentation. Programs for TI
graphing calculators and additional computer software on material covered in MA 181 are available in the
Math/Science Center either for student use or for demonstration. For more information, contact the
Math/Science Center.
SUPPLEMENTS: The text comes with an instructor's guide. The authors of the guide suggest that instructors
read it along with the text. It can be used as a source of additional material, and also contains suggestions
regarding points to stress in each section, various approaches to the material, group work activities,
recommended homework problems, and usage of TEC (Tools for Enriching Calculus) accessible on
www.stewartcalculus.com. The guide also includes sample test questions for each chapter.
Numerous other ancillaries and resources also accompany the text. For a description, please see the
preface of the book. In addition, various lab manuals for technology use are also available. These include
manuals for the TI-82/83, TI 85/86, Derive and Maple. If you would like a copy of any of these, or of any of
the ancillaries listed in the preface, please contact the Department Administrative Aide, Janice Burke (240567-5194).
The Power Lecture with Exam View DVD contains PowerPoint lecture notes, PowerPoint images, videos, a
testbank for the creation of customized tests, an image library, and an instructor’s guide.
ENHANCED WEBASSIGN (EWA): An online homework system with free response, multiple choice, and multipart question formats. Instructors can set up their own course and create assignments or use the course set
up by the MA 181 Course Chair. EWA is NOT packaged with the text at the Rockville campus bookstore.
Students who want to purchase EWA can go to www.cengagebrain.com/shop/index.html and enter ISBN:
0538738111
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Coursesmart (http://instructors.coursesmart.com/learnmore) is a way for instructors to access the textbook online.
This site is especially helpful in the smart classrooms if you want to display the electronic version of the text using the
computer at the smart workstation.
(5)
Chp
If you find any errors in the text or in any of the ancillaries, or if you have suggestions for changes to
the course outline, please let me know.
Suggested #
of 75-minute
periods
Topic/Sections
Diagnostic Tests
The beginning of the book contains four diagnostic tests in basic algebra, analytic
geometry, functions, and trigonometry. Answers are given in the same section,
and students who do not do well are referred to the Appendix, review sections in
Chapter 1, and the website stewartcalculus.com.
A Preview of Calculus
Discuss one or two of the "classic" Calculus problems in class or assign for reading.
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Functions and Models
Since most of the material in this chapter is covered in MA 180 (Precalculus), this
material can be treated in a variety of ways:
 Spend little or no time on review at the beginning of the semester and
incorporate review on as needed basis during the semester, using whatever
extra time is gained on optional topics and/or more in-depth exercises.

Review some sections in detail, highlighting skills which will be needed later in
the semester. The material in 1.3 on transformations, combinations, and
compositions of functions is thoroughly treated in MA 180, and only
composition of functions is critical later in MA 181 when the Chain Rule is
discussed. Section 1.5, Exponential Functions, is also covered thoroughly in
MA 180. Instructors should be sure that students are familiar with these
functions but should not spend time on problems involving exponential
growth and decay. Also note that trigonometric and inverse trigonometric
functions are discussed in Appendix C. Trigonometric functions can be briefly
reviewed in class (along with 1.2, where they are mentioned briefly), assigned
for reading or deferred to 3.3, Derivatives of Trigonometric Functions.
Similarly, inverse trigonometric functions can be covered along with 1.6
(inverse functions), or deferred to 3.6, where the formulas for their
derivatives are developed, and 1.7 Parametric Curves can be deferred to 3.4
when derivatives of parametric curves (an optional topic) are discussed.

Have students work on selected exercises, either in class or as homework and
provide assistance when needed.

Assign material for reading, assign exercises, and provide an opportunity for
questions.
4
0 – 0.5
0–4
2
Limits and Derivatives
Section 2.1 motivates the concept of limit by a discussion of tangent lines and
velocity. If you wish to plunge right into limits, 2.1 could be covered just before
2.6. Limits are treated from descriptive, graphical, numerical, and algebraic points
of view.
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The formal definition of limit is given in Appendix D and is optional.
3
Differentiation Rules
All basic functions are differentiated here. Section 3.8, Rates of Change in the
Natural and Social Sciences, uses applications that incorporate the differentiation
rules discussed in the first seven sections of Chapter 3.
8.5
Optional: Derivatives of parametric curves in 3.5, logarithmic differentiation in
3.7.
4
Applications of Differentiation
The basic facts concerning extreme values and shapes of curves are derived using
the Mean Value Theorem as the starting point. Graphing with technology
emphasizes the interaction between calculus, calculators, and the analysis of
families of curves. Applications encompass related rates problems, optimization
problems, and Newton’s Method.
8.5
Omit 4.5 (Indeterminate Forms and L'Hospital's Rule); this material will be covered
in MA 182.
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Integrals
The area problem and the distance problem serve to motivate the definite
integral.
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Cover Sections 5.1 - 5.4 only; the rest will be covered in MA 182.
It is essential that all of this material be covered. In order to be certain of having
enough time to do so, instructors can consider deferring some earlier material
until the end of the semester. For example, Section 4.1, Related Rates, is
essentially independent of the rest of Chapter 4 and can be covered after Sections
5.1 - 5.4.
Optional: The use of summation formulas to evaluate definite integrals in Sections
5.1 and 5.2
Optional topics and/or more in-depth exercises
1.5
Tests and Review
6/42
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SUGGESTED TEXTBOOK EXERCISES
Section
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
4.2
4.3
4.4
4.6
4.7
4.8
5.1
5.2
5.3
5.4
4.1
Page
94
102
111
121
132
142
155
162
181
188
195
205
214
220
226
237
245
268
279
288
305
315
321
341
353
363
373
260
Exercises
1 – 9 odd
1 – 21 odd, 27
1  3, 5, 7, 8, 9 – 29 odd, 33, 35, 37, 39
1 – 8, 9, 11, 13, 15, 17, 19, 21, 25, 27, 31, 33, 35, 37, 43, 49
1, 3, 5, 7, 9, 13, 15, 19, 21, 25, 27, 31, 35
1  3, 5, 7, 9, 11, 13, 15, 17, 19, 23, 29, 37, 41, 43, 47, 51
1, 3, 5, 9, 11, 21, 25, 33, 35, 37, 41, 43
1, 3, 5, 7, 9, 10, 11, 12, 15, 17, 19, 21, 23, 25, 27, 29, 31
1, 3, 5, 7, 11, 15, 19, 25, 27, 29, 31, 41, 45, 49, 51,
1, 3, 5, 7, 13, 21, 25, 27, 29, 31, 33, 35, 41, 43, 45, 47, 49, 51
1, 5, 9, 11, 13, 19, 21, 23, 27, 31, 33, 35, 37
1, 3, 5, 7, 9, 17, 19, 21, 23, 29, 37, 41, 43, 45, 47, 49, 51, 53, 55, 59, 61, 69, 71, 73, 79
1, 7, 9, 13, 15, 17, 19, 21, 25, 27, 29, 31
17, 19, 21, 23, 25,
1, 3, 7, 11, 13, 19, 21, 27, 29, 31, 33, 39,
1, 3, 5, 9, 11, 13, 15, 17, 19, 23, 25, 27
1, 3, 5, 7, 9, 15, 19, 27, 29, 35
1  3, 5, 7, 9, 11, 13, 25, 29, 33, 35, 37, 43, 47, 49, 51, 53, 61
1  3, 5, 6, 7  13 odd, 17, 19, 25, 27, 29, 31, 33, 37, 41, 49
1, 3, 5, 15,
5, 7, 9, 11, 13, 15, 19, 23, 25, 31, 37
1, 3, 7, 11, 13, 15, 21, 25, 29,
1, 3, 7, 9, 11, 13, 15, 17, 19, 25, 27, 29, 31, 35, 41, 43, 49, 51, 53
1, 3, 5, 7, 11, 13, 15, 17
1, 3, 5, 7, 9, 17, 21, 29, 31, 35, 37, 47
3, 7, 11, 15, 19, 23, 25, 27, 39, 41, 43, 47, 51, 53, 55, 57, 59, 63
1, 3, 5, 7, 11, 13, 19, 21, 23
3, 5, 9, 11, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37
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Websites
My MA 181 website can be accessed from my homepage at
http://www.montgomerycollege.edu/~iscott/ma181.html
You can access my handouts through this website. Please feel free to make use of this material in any way.

stewartcalculus.com
This is the website for all of the Calculus books by Stewart. If you go to it, choose the link for Calculus, Concepts
and Contexts. You may find it useful to go to Chapters, where you will find a web quiz and links for each
chapter.

montgomerycollege.edu/~rpenn/Main.htm
This website was written by Professor Rick Penn. It is an excellent source for a variety of problems which
students can use for practice. For MA 181, the relevant links are Limits, Derivatives (Graphical), Derivatives
(Analytical), and Integrals. For Integrals, students should choose Basic Integrals only.

wolframalpha.com
A free web-based computer algebra system [based on Mathematica software] that provides answers to
questions typed into a simple search box, step-by-step solutions, graphs, and more.

Calculus Modeling & Application, 2nd Edition http://www.math.duke.edu/education/calculustext/
A first-year online interactive calculus book that incorporates hands-on activities, discovery learning, realworld applications, and writing. Currently freely available. Click here for more information about the text.

calc101.com
Students can go to this site to get step-by-step derivatives and integrals, with each step explained. The
students can choose "dead examples" (pre-determined problems) or "live solutions" (examples which are put
in by the student). Derivatives are free, but for "live" integrals, the students must purchase a password (valid
for 900 solutions) for $30. This site could be useful for students who would like more examples for which they
can see step-by-step solutions.

cow.math.temple.edu
Calculus on the Web (COW) consists of a series of modules from pre-calculus to linear algebra. The student
must provide an answer to a problem or to one step of a problem and can immediately find out if the answer is
correct. The student can also click the "help" option to obtain either a general discussion of the type of
problem or a complete solution of the problem given. This site could be useful for students who would like
more examples for practice. It is more comprehensive than the previous site, but students cannot make up
their own examples.

http://www.ies.co.jp/math/products/calc/menu.html
This website leads to a collection of Calculus applets, divided into three categories - limits, derivatives and
integrals. One applet, which I like for demonstration purposes is "Surfing (Derivatives)."

http://tutorial.math.lamar.edu/
This website provides a complete set of free online (and downloadable) notes and/or tutorials.
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
http://archives.math.utk.edu/visual.calculus/
This website contains a collection of modules that can be used in the studying or teaching of calculus.

Calculus Writing Prompts
A list of almost 750 calculus writing prompts

HippoCampus http://www.hippocampus.org/Calculus;jsessionid=A3E413FC33457DC43A799BCD827264C9
Hippocampus is free, public website for high school and college students that offers National Repository of
Online Courses (NROC) multimedia correlated to most major textbooks.
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