FALL 2010
CALCULUS 1, MA280-05
M, R, F; 11:00-11:50; IRALL003
T; 11:00-11:50; ANXCN 103
Instructor name: Prof. Anita Penta
Office location: IRALL214
Office telephone number: 617 989 4351
Office hours and Location: M, T, R 10:00 - 11:00
Email address: pentaa@wit.edu
Credits/Hours: 4-0-4
______________________________________________________________________________
COURSE DESCRIPTION:
Introduction to limits, definition of the derivative, differentiation of algebraic
and transcendental functions, implicit differentiation and applications of the
derivative. Course concludes with an introduction to integration of algebraic
and transcendental functions, the fundamental theorem of calculus, and area.
REQUIRED TEXTBOOK(s):
The text is Calculus with Early Transcendentals (1st edition) by Hass, Weir and
Thomas with MyMathLab. Published by Pearson. See the attached outline for
chapter references and other details.
THE COLLEGE BOOKSTORE:
Location:
103 Ward Street Boston MA 02115
Telephone: 617-445-8814
RECOMMENDED LEARNING MATERIALS:
A standard graphing calculator is encouraged. Calculators with a CAS
(computer algebra system) will not be permitted.
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COURSE LEARNING OUTCOMES:
I. Functions and Limits




Find
Find
Find
Find
the average rate of change over an interval.
limits graphically.
limits algebraically.
where a function is continuous graphically.
II. Differentiation
 Know basic concepts of inverse functions.
 Know basic concepts of logarithms.
 Find the slope and tangent lines for polynomial functions using the
limit definition of the derivative.
 Graphically find points where the function is differentiable.
 Find the derivative of algebraic functions.
 Find derivatives of trigonometric functions.
 Find the derivative of inverse trigonometric functions.
 Find the derivative of the logarithmic function.
 Find the derivative of the exponential function.
 Find higher order derivatives.
 Find the derivative of composite functions.
 Use implicit differentiation.
 Use logarithmic differentiation.
 Find the differential.
 Find the slope, the equation for the tangent line and the normal line.
 Find the body’s displacement and average velocity.
 Solve free fall applications.
 Find the velocity, speed, acceleration and jerk of a body in simple
harmonic motion.
 Solve related rates applications.
III. Integration
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 Find indefinite integrals of basic algebraic, trigonometric, and
exponential functions.
 Evaluate definite integrals using the Fundamental Theorem of
Calculus.
 Find the area of regions using definite integrals.
 Solve initial value problems.
IV. Applications of Derivatives
 Find critical points, increasing and decreasing intervals, and local and
absolute extrema using the First Derivative Test.
 Find inflection points and intervals of concavity using the Second
Derivative Test.
 Solve optimization applications.
INSTRUCTIONAL METHODOLOGIES:
Classroom instruction is interactive, beginning each day with a discussion of
difficulties and questions encountered in the daily homework assignment. New
topics are introduced through problem solving, using applications in which the
topics arise as motivation. Classroom discussion elicits the fundamental
difficulties of the application and suggests means for their solution. Each
investigation is followed by nightly homework exercises that are completed
online using the MyMathLab software package. Periodic examinations, that are
taken in class and are not online, require students to demonstrate their level of
mastery.
ATTENDANCE POLICY:
Any student missing 15% of scheduled classes may be withdrawn according to
the attendance policy. Refer to the Student Handbook for details. If you miss
a class for any reason, it is your responsibility to check on any announcements
that were made.
GRADING POLICY:
Homework:
Homework will be assigned daily on MyMathLab. Homework done on
time will receive extra credit at the end of the term. Up to four points will be
added to your final average. In order to receive any extra credit your
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homework average has to be greater than 60%.
Tests:
There will be at least four one-hour tests. The dates will be announced
in class. Each test is worth 100 points. A final exam will be scheduled
during finals week. The final exam will also be worth 100 points. The lowest
test will be dropped at the end of the term. Should an emergency force you to
miss a test, that test will be the one that is dropped.
Quizzes:
There will be some short quizzes. Each quiz is worth 10 points. There
are no make-ups to any quiz. The lowest quiz grade will be dropped at the end
of the semester. Should an emergency force you to miss a quiz, that quiz will
be the one that is dropped.
Wentworth Grading System:
Grade Definition
Weight
Numerical
A
Student learning and accomplishment
4.00
96-100
A-
far exceeds published objectives for the
course/test/assignment and student work
is distinguished consistently by its high
level of competency and/or innovation.
3.67
92-95
B+
Student learning and accomplishment
3.33
88-91
B
goes beyond what is expected in the
3.00
published objectives for the course/test/
assignment and student work is frequently
characterized by its special depth of
understanding, development, and/or innovative
experimentation.
84-87
BC+
Student learning and accomplishment
meets all published objectives for the
2.67
2.33
80-83
76-79
C
course/test/assignment and student
work demonstrates the expected level of
understanding, and application of concepts
introduced.
2.00
72-75
C-
Student learning and accomplishment
1.67
68-71
4
D+
based on the published objectives for
1.33
64-67
D
the course/test/assignment were met
with minimum passing achievement.
1.00
60-63
F
Student learning and accomplishment
based on the published objectives for than 60
the course/test/assignment were not
sufficiently addressed nor met
0.00
Less
DROP/ADD:
The drop/add period for day students ends on Friday of the first week of
classes. Dropping and/or adding courses is done online. Courses dropped in
this period are removed from the student’s record. Courses to be added that
require written permission, e.g. closed courses, must be done using a
Drop/Add form that is available in the Student Service Center. Non-attendance
does not constitute dropping a course. If a student has registered for a course
and subsequently withdraws or receives a failing grade in its prerequisite, then
the student must drop that course. In some cases, the student will be
dropped from that course by the Registrar. However, it is the student’s
responsibility to make sure that he or she meets the course prerequisites and
to drop a course if the student has not successfully completed the prerequisite.
The student must see his or her academic advisor or academic department
head for schedule revision and to discuss the impact of the failed or withdrawn
course on the student’s degree status.
MAKE-UP POLICY:
See the above grading policy. Should an emergency force you to miss a test,
this will be the one that is dropped. Should an emergency force you to miss a
quiz, this will be dropped
ACADEMIC SUPPORT:
The Center for Teaching and Learning (CTL) assists all Wentworth students
with academic challenges in the areas of math, science, technical courses
specific to majors, and writing. The CTL is a supportive and safe learning
environment for students looking to improve or maintain their academic
standing. In this student-based learning environment, students can receive
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individual help with their studies, meet and work in study groups, or go on-line
to find resources to assist them in meeting their goals for academic success. It
includes tutors in many subjects, online writing assistance and workshops.
Make appointments at www.wit.edu/academics/resources or through
Lconnect.
ACADEMIC HONESTY STATEMENT:
“Students at Wentworth are expected to be honest and forthright in their
academic endeavors. Academic dishonesty includes cheating, inventing false
information or citations, plagiarism, tampering with computers, destroying other
people’s studio property, or academic misconduct” (Academic Catalog). See your
catalogue for a full explanation.
STUDENT ACCOUNTABILITY STATEMENT:
Cheating is not tolerated and will result in failure (Refer to the Student
Handbook).
DISABILITY SERVICES STATEMENT:
Any student who thinks s/he may require a disability-related accommodation
for this course should contact me privately to discuss your specific needs.
Disability Services coordinates reasonable accommodations for students with
documented disabilities. They are located in Watson Hall 003 (the Counseling
Center) and can be contacted at 617-989-4390 or counseling@wit.edu. For
more information on acceptable documentation and the Disability Services
process, visit the Disability Services website at www.wit.edu/disabilityservices
ASSIGNMENTS:
Homework will be assigned daily on MyMathLab. Homework done on time
will receive extra credit at the end of the term. Up to four points will be
added to your final average. In order to receive any extra credit your
homework average has to be greater than 60%.
WENTWORTH INSTITUTE OF
TECHNOLOGY
DEPARTMENT OF APPLIED MATHEMATICS AND SCIENCES
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MATH 280 CALCULUS I: Syllabus
I. Functions and Limits
Sec 1.3 Rates of Change and Tangents to Curves
 Find the average rate of change over an interval.
 Find the equation of a tangent line at a point.
Sec 1.4 Limit of a Function and Limit Laws
 Find limits graphically.
 Find limits by eliminating zero denominators algebraically.
Sec 1.6 One-Sided Limits
 Find limits graphically.
Sec 1.7 Continuity
 Determine where a function is continuous graphically.
II. Differentiation
Sec 2.1 Tangents and Derivatives at a Point
 Find the slope and tangent lines for polynomial functions using
the limit definition of the derivative.
Sec 2.2 The Derivative as a Function
 Graphically find points where the function is differentiable.
Sec 2.3 Differentiation Rules
 Find the derivative of the function.
 Find higher order derivatives.
 Solve applications.
Sec 2.4
The Derivative as a Rate of Change
 Find the body’s displacement and average velocity.
 Solve free fall applications.
 Solve application problems.
Sec 2.5
Derivatives of Trigonometric Functions
 Find derivatives of trigonometric functions.
 Find the equation for the tangent to the curve.
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 Find the velocity, speed, acceleration and jerk of a body in
simple harmonic motion.
Sec 2.6 Exponential Functions
 Find the first and second derivatives of the function.
Sec 2.7
The Chain Rule
 Find the derivative of composite functions.
 Solve application problems.
Sec 2.8
Implicit Differentiation
 Use implicit differentiation.
 Find the slope, the tangent line, or the normal line.
Sec 2.9 Inverse Functions and Their Derivatives
 Review basic concepts of inverse functions.
Sec 2.10
Logarithmic Functions




Sec 2.11
Review basic concepts of logarithms.
Find the derivative of the logarithmic function.
Use logarithmic differentiation.
Find the derivative of the exponential function.
Inverse Trigonometric Functions
 Find the derivative of inverse trigonometric functions.
Sec 2.12
Related Rates
Sec 2.13
Linearization and Differentials
 Solve related rates applications.
 Find the differential.
III. Integration
Sec 4.1 Antiderivatives
 Find an antiderivative or indefinite integral.
 Solve initial value problems.
Sec 4.5 The Fundamental Theorem of Calculus
 Evaluate the integral.
 Find the total area between the region and the x-axis.
 Find the area of the shaded region.
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IV. Applications of Derivatives
Sec 3.3 Monotonic Functions and The First Derivative Test
 Find critical points, increasing and decreasing intervals, and
local and absolute extrema.
Sec 3.4 Concavity and Curve Sketching
 Find inflection points and intervals of concavity using the
Second Derivative Test.
Sec 3.6 Applied Optimization
 Solve applications.
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