Patrick Henry Community College
MTH 175 Calculus of One Variable
Fall 2016
INSTRUCTOR: Cynthia M. Cowley
OFFICE LOCATION: NCI, 191 Fayette St. 2
nd
Floor
OFFICE HOURS: M-F 12:30 – 3:00 P.M., or by appointment
OFFICE PHONE: 276-403-5633
CELL PHONE: 276-340-7919
E-MAIL ADDRESS: [email protected] or [email protected]
CLASS MEETING TIME: M/W 9:30 – 11:05 A.M. ; T/Th 9:30 – 11:05
CLASSROOM LOCATION: NCI room 208
COURSE CREDITS: 3
PREREQUISITE(S): a placement recommendation for MTH 175 and four units of high school
mathematics including Algebra I, Algebra II, Geometry and Trigonometry or equivalent.
COURSE DESCRIPTION
This course presents differential calculus of one variable including the theory of limits, derivatives,
differentials, anti-derivatives and applications to algebraic and transcendental functions. It is designed for
mathematical, physical, and engineering science programs.
COURSE INTRODUCTION
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Calculus was developed in the 17 century independently and simultaneously by Sir Isaac Newton and G.
W. Leibniz. They actually argued over the ownership of calculus for 25 years. It has now been
established that Newton developed calculus first, but Leibniz was the first to publish on the subject. The
applications of calculus occurs in many disciplines: to compute the gravitational force of an object near
the surface of the earth in physics; to compute reaction rates in chemistry; to model population growth in
biology and sociology; and to model compound interest in economics. This course is a culmination of all
high school math courses; therefore, a solid foundation in the prerequisite courses is essential.
A. COURSE OBJECTIVES
Upon successful completion of this course, the student should:
Ø Develop effective study skills in order to master course content and objectives.
Ø Demonstrate an understanding of the basic mathematical skills used in calculus.
Ø Communicate clearly and effectively the principles of calculus using proper vocabulary.
Ø Apply the principles and concepts of calculus to solve practical problems in mathematics.
Ø Work with functions represented in a variety of ways and understand the connections among
these representations.
Ø Understand the meaning of the derivative in terms of a rate of change and local linear
approximation, and be able to use derivatives to solve a variety of problems.
Ø Understand the meaning of the definite integral both as a limit of Riemann sums and as the net
accumulation of change and be able to use integrals to solve a variety of problems.
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Understand the relationship between the derivative and the definite integral as expressed in both
parts of the Fundamental Theorem of Calculus.
Model a written description of a physical situation with a function, a differential equation, or an
integral.
Use technology to help solve problems, experiment, interpret results, and verify conclusions.
Determine the reasonableness of solutions, including sign, size, relative accuracy, and units of
measurement.
Develop an appreciation of calculus as a coherent body of knowledge and as a human
accomplishment.
Prerequisites to Calculus (3 days)
(Sections 1.1, 1.2, 1.3, 1.5, 1.6, C.3)
• Graphs and models
• Linear models and rates of change
• Functions and their graphs
• Inverse functions
• Exponential and logarithmic functions
• Review of trigonometric functions
Unit 1 – Limits and Their Properties (7 days)
• Finding limits graphically and numerically (Section 2.2)
• Evaluating limits analytically (Section 2.3)
• Continuity and one-sided limits (Section 2.4)
• Infinite limits and limits involving infinity (Sections 2.5 and 4.5)
• Asymptotic and unbounded behavior (Sections 2.5 and 2.5)
• Understanding asymptotes in terms of graphical behavior (Sections 2.5 and 4.5)
• Describing asymptotic behavior in terms of limits involving infinity (Section 4.5)
• Geometric understanding of graphs of continuous functions (Intermediate Value Theorem and
Extreme Value Theorem) (Sections 2.4 and 4.1)
Unit 2 – Differentiation (16 days)
• The concept of the derivative presented geometrically, numerically, and analytically (Section 3.1)
• Definition of derivative: limit of the difference quotient (Section 3.1)
• The tangent line problem (Section 3.1)
• Slope of a curve at a point (Section 3.1)
• Basic differentiation rules, velocity, and other rates of change (Section 3.2)
• Product Rule, Quotient Rule, and higher order derivatives (Section 3.3)
• Derivatives of trigonometric functions (Section 3.3)
• Derivatives of logarithmic and exponential functions (Sections 3.2 and 3.4)
• Chain Rule ( Section 3.4)
• Differentiating functions involving radicals (Section 3.4)
• Implicit differentiation (Section 3.5)
• Logarithmic differentiation (Section 3.5)
• Derivatives of inverse functions (Section 3.6)
Unit 3 – Applications of Differentiation (18 days)
• Extrema on an interval (Section 4.1)
• Rolle’s Theorem and The Mean Value Theorem (Section 4.2)
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Increasing and decreasing functions and the First Derivative Test (Section 4.3)
Concavity and the Second Derivative Test (Section 4.4)
Corresponding characteristics of graphs of 𝑓 and 𝑓′ (Section 3.3)
Relationship between the increasing and decreasing behavior of 𝑓 and the sign of 𝑓′ (Section 3.3)
Corresponding characteristics of the graphs of 𝑓, 𝑓 $ , and 𝑓" (Section 3.4)
Relationship between the concavity of 𝑓 and the sign of 𝑓" (Section 3.4)
Finding points of inflection (Section 3.4)
Graphing summary including zeros, domain and range, asymptotes, symmetry, extrema, and
concavity (Section 4.6)
Optimization problems (Section 4.7)
Modeling rates of change, including related-rates problems (Section 3.7)
B. VCCS CORE COMPETENCIES
Degree graduates will demonstrate the ability to
1.1 Understand and interpret complex materials;
2.6 Use problem solving skills;
4.1 Determine the nature and extent of the information needed;
4.2 Access needed information effectively and efficiently;
6.1 Use logical and mathematical reasoning within the context of various disciplines;
6.2 Interpret and use mathematical formulas;
6.3 Interpret mathematical models such as graphs, tables and schematics and draw inferences
from them;
6.4 Use graphical, symbolic, and numerical methods to analyze, organize, and interpret data;
6.5 Estimate and consider answers to mathematical problems in order to determine
reasonableness; and
6.6 Represent mathematical information numerically, symbolically, and visually, using graphs and
charts.
C. METHOD OF INSTRUCTION
A variety of instructional methods will be utilized. As a group we will work extensively on study habits,
appropriate use of the graphing calculators, and student communication – both oral and written. Students
will be encouraged to actively participate in the learning process to help ensure that they understand the
material. Many examples will be provided through lecture and class activities. The use of e-mail /
Blackboard is essential.
D. TEXTBOOK(S) AND REQUIRED TOOLS OR SUPPLIES
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Calculus of a Single Variable: Early Transcendental Functions, 5 edition
Ron Larson & Bruce Edwards
Brooks/Cole, 2011
Additional student resources are available via the on-line version, and the website www.CalcChat.com
Supplies
• Pencils
• One 2-3” 3-ring binder to include notes, homework, quizzes, tests, free response problems,
projects
• Dividers for 3-ring binder (one set with 6 tabs labeled with the categories listed above)
• Loose-leaf paper (lots!)
• Graph paper (optional)
• TI-84 Graphing calculator
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E. STUDENT EVALUATION
Students will be assessed in various ways, including, but not limited to daily homework assignments,
quizzes, tests, projects, group activities, and free-response questions. All work submitted to the instructor
must be in pencil.
Grades will be based on the following:
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Homework: 15%
This grade is based on daily checks for completion; homework should be kept in a three-ring
binder, organized chronologically by date with the page number of the assignment included at the
top of the paper. Score will be determined using the following rubric:
Score
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4
3
2
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0
Criteria
Assignment 90% or more completed before arriving to class. Full work and solutions
shown. Questions written down when you are stuck on a problem.
Assignment 80% or more completed before arriving to class. Full work and solutions
shown. Questions written down when you are stuck on a problem
Assignment 60% or more completed before arriving to class. Full work and solutions
shown. Questions written down when you are stuck on a problem.
Less than 60% of the problems attempted.
Less than 30% of the problems attempted.
No problems attempted.
When you don’t know how to solve a problem, you must make an attempt to start it and then write
down specific questions you have about how to continue solving the problem. Just writing a
question mark ‘?’ or stating ‘I don’t know what to do’ will not get you credit for the problem.
Use questions like:
Should I use the chain rule to differentiate?
Do I factor to find the solutions, or do I use the quadratic formula?
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Quizzes: 20%
One or two closed-book quizzes will be given in each unit, usually covering two or three sections
of the chapter. Projects will be assigned periodically and will count as a quiz grade.
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Free-response questions (FRQs): 20%
Beginning midway through the first grading period, free-response questions (which cover multiple
concepts) will be assigned. Students will have a week to complete these assignments, and they
should write their solutions to these problems according to guidelines provided by the instructor.
The assignments will be graded on a nine-point scale following the AP grading rubric and will be
due by 7:45 A.M. Friday of the week the assignment was given, unless otherwise stated. Papers
will not be accepted after midnight of the due date; there are no exceptions. Papers submitted
after 7:45 A.M., but before midnight, will incur a point deduction based on a pro-rated scale. If
the student does not report to Governor’s School that morning, he/she must scan and email the
assignment to the instructor by 7:45 A.M.
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Tests: 45%
A test will be given at the end of each unit. Tests are a combination of multiple choice and freeresponse questions taken from old AP exams. For some questions, no calculator is allowed;
however, for some a calculator is required.
An exam will be given at the end of the semester and will count 25% of the final semester grade.
F. GRADING SCALE:
A
90 - 100
B
80 - 89
C
70 - 79
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D
F
60 – 69
59 - below
G. EXPECTATIONS FOR STUDENT SUCCESS
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Be present for each class
o Students should attend class daily; seven absences will lower final grade by one letter
grade. Three tardies or three early dismissals equal one absence. A student must be in
class at least one hour to be counted present for that class.
o Students should email the instructor when missing a class, thus setting plans in motion
for the lesson to be recorded for them. Attach to the email one document including the
homework assignment that was due that day.
o Students should submit note to Mrs. East within 24 hours of the student’s return with a
valid reason for student’s absence. No make-up work will be allowed for unexcused
absences.
o Students should see instructor the day returning from a missed class to ask questions
pertaining to the lecture and/or assignment.
o Students should make arrangements to make up quiz/test if missed due to absence.
Submit all work on time.
o Students should submit all work by the due date. Assignments other than homework and
FRQs not submitted by the due date will incur a 25-point deduction per day after the due
date. Homework is due at the next class meeting (after it was assigned) will not be
accepted after the due date, and FRQs are not accepted after midnight of the due
date (as explained earlier in the syllabus).
o Work that is to be submitted on Bb should be uploaded in the Assignment Tab for the
specified assignment. The work must be converted to a Word document and submitted
in one attachment.
§ To submit assignments on Bb, click on the link for the assignment, then upload
the file, preview the file to ensure that all portions or problems are present, then
click the “submit” icon.
Create a fun learning environment.
o Students may have drinks in the classroom, provided the drink has a screw-on cap and
fits in the receptacle attached to the student desk. Students must leave their area clean.
o Students should show respect for classmates and instructor, listen carefully, and not
interrupt someone who is talking.
o Cell phones may not be used in class unless permission is given by the instructor.
Phones must be placed in silent mode and placed in the designated area upon entering
the classroom.
WHAT A STUDENT CAN EXPECT FROM THE INSTRUCTOR
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On any day that a student is absent from class, the lesson will be recorded and posted on
Blackboard or emailed to the student(s).
Homework emailed to the instructor upon a student’s absence from class will be assessed and
returned to the student during the next class meeting.
The instructor will evaluate and return quizzes and tests work promptly with feedback.
The instructor will be available before school between 7 and 7:30 A.M., between classes, and
after governor’s school for tutoring.
Tutoring is available at other times by appointment.
Afternoon/evening study sessions will be scheduled throughout the year as needed.
Continuous support, assistance, and TLC.
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H. EMERGENCY INFORMATION
In case of emergency, students should exit the classroom and leave the building by way of the stairwell to
the right of the classroom.
I. STUDENT SUPPORT/DISABILITY STATEMENT: Patrick Henry Community College makes every
effort to accommodate individuals with disabilities for all programs, services, and activities available to the
public.
J. IMPORTANT DATES TO REMEMBER:
School calendar is available in the student handbook and at the following site: www.pgsmst.com
K. SPECIFIC COLLEGE POLICIES
Academic Honesty
Students are expected to abide by the code of conduct and academic integrity found in the student
handbook. Students will be required to sign a pledge on any take-home quizzes/tests stating “On my
honor, I have neither given nor received aid on this assignment.” Infractions of the honor code will not be
tolerated and will be reported to the director and will be addressed with the student and his/her parents.
All violations of academic integrity will also be reported to each student’s honor organization.
Inclement Weather
If Henry County schools are delayed one hour, Governor’s School will open one hour late. One common
question asked is “If my base school is closed but roads in my residential area are clear, should I come to
Governor’s School?” The decision to attend under those circumstances should be made by the parent(s).
If Henry County schools are delayed two hours, Governor’s School classes will be cancelled. If Henry
County schools are closed, Governor’s School is closed and classes do not meet. Henry
County/Martinsville work days do not impact classes at Piedmont Governor’s School.
• Assignments and/or lectures may be posted on Blackboard on days when Governor’s School
classes are affected by inclement weather. It is the student’s responsibility to check Blackboard
and complete the assignments before their next class meeting.
• A link will be established on Bb where students should submit homework that is due on a day
where governor’s school is cancelled. Homework should be posted by 12 noon of the day the
assignment is due.
Internet Resources
http://www.collegeboard.com/student/testing/ap/calculus_ab/samp.html?calcab
www.hotmath.com
www.mathwords.com/index_calculus.htm
www.CalcChat.com
L.
is an online tutoring service which gives students 24/7 access to highly
qualified, experienced, and specially trained tutors. Virtual whiteboard technology lets students and tutors
share the same screen. Students may submit writing assignments to be evaluated / proofread. All live
sessions with tutors and submitted questions are saved so students can view or print them out. Any
PHCC student can access Smarthinking free of charge. Smarthinking can only be accessed through
BlackBoard. Further information may be obtained from your instructor or the Writing Center Tutors.
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