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Information |
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Course Description: |
This course
is a study of differential calculus with an introduction to integration.
Topics covered will include plane analytical geometry, limits,
continuity, and the derivative and integral of functions of one variable
with applications.
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Course Objectives: |
Goals:
- to understand and apply the concepts of
continuity and limit of a function both intuitively and precisely, by use
of their definitions;
- to understand and apply the definition
and methods of differentiation of algebraic functions;
- to use the derivative in sketching the
graphs of algebraic functions and relations;
- to apply the derivative to specific
modeling problems involving, for example, motion, optimization, and
related rates;
- to understand and apply the Fundamental
Theorem of Calculus;
- to understand and apply the concept of
integration, show its application to
area under curves, and practice basic integration techniques;
- to fulfill the mathematics requirement
for those students required to take only MATH 1910 as well as to prepare
those students who are required to take MATH 1920; and,
- to promote better understanding of
concepts introduced throughout the course by the appropriate use
technology.
Objectives:
- examine and determine by tables and
graphs whether or not the limit of a function exists at a given value
of x and if so, find that limit;
- apply the formal e, δ definition of
a limit;
- discuss general properties of the
limits of algebraic functions; examine techniques and strategies such
as substitution, graphing, cancellation, and rationalizing for
evaluating limits;
- indicate whether a given function is
continuous or discontinuous at a given value of x or on an interval
containing x and examine removable and non-removable discontinuities;
- evaluate one-sided limits and
discuss their relationship to the ideas of continuity;
- graph and investigate the greatest
integer function and compound functions in relation to limits and
continuity;
- evaluate infinite limits by graphic
and algebraic processes and discuss their relationship to vertical and
slant asymptotes;
- find the slope of a curve at point A
by use of the slope of a secant line through A and another point on
the curve near A;
- find the derivative of a function by
use of the definition and discuss the relationship between
differentiability and continuity;
- write the equation of the line
tangent to a given curve at a given point;
- differentiate functions using basic
rules and apply to simple motion problems;
- differentiate algebraic using
product, quotient, chain and general power rules and evaluate at given
values of x;
- find the derivative of a function
using implicit differentiation;
- find the higher order derivatives of
functions by both explicit and implicit differentiation and apply to
equations of motion;
- apply differentiation processes to
related rates problems;
- find critical numbers and locate
extrema of a function on an interval, including endpoints;
- state Rolle's Theorem and the Mean
Value Theorem and apply for given functions;
- determine intervals over which a
curve is increasing or decreasing and determine relative maximum and
minimum values of given functions by use of the first derivative;
- determine intervals of concavity,
find points of inflection, and test for maxima and minima by use of
the second derivative;
- evaluate limits at infinity
graphically and algebraically and discuss their horizontal asymptotes;
- sketch the graphs of given functions
by use of intercepts, asymptotes, symmetry, and information obtained
by use of the first and second derivatives;
- apply derivatives to solve
optimization problems;
- use Newton's method to find zeros of
functions;
- understand and find differentials of
functions and apply to determining error;
- define anti-differentiation and find
the anti-derivative of given polynomial,
power, and rational functions;
- use anti-derivatives to find the
equation of motion when given acceleration or velocity of a particle
at a given time;
- perform operations with sigma
notation and use it to find the area under the graphs of certain
polynomial functions by using rectangular subdivisions;
- study properties of the definite and
indefinite integral;
- study the Fundamental Theorem of
Calculus and use to evaluate definite
integrals of polynomial and other algebraic relations and
transcendental functions, and apply to finding the area under curves;
and,
- evaluate indefinite and definite
integrals of algebraic expressions by using substitution procedures
and the general power rule for integration.
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Prerequisites
and Corequisites: |
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Documented eligibility for collegiate
mathematics; high school credits in college preparatory mathematics to
include Algebra I, Algebra II, geometry, and trigonometry or MATH 1710
and MATH 1720 or equivalent.
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Course Topics:
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- Functions
and Models (weeks one and two)
- Limits and
Rates of Change (weeks three and four)
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Derivatives (weeks five, six, and seven)
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Applications of Derivatiation (weeks eight, nine, and ten)
- Integrals
(weeks eleven and twelve)
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Applications of Integration (weeks thirteen, fourteen, and fifteen)
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Specific Course Requirements:
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Students
will be required to learn and use a graphing calculator, install free
browser plug-ins, and install and use free downloadable mathematics
software.
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Textbooks, Supplementary Materials, Hardware and Software Requirements |
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Required
Textbooks:
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Supplementary Materials:
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A graphing
calculator is highly recommended. The Texas Instruments TI-83, TI-83 Plus,
and/or TI-89 will be used in demonstrations. Other
graphing calculators may work but will not be supported by the
instructor.
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Hardware
Requirements:
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Software
Requirements:
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The minimum
requirements can be found at
http://www.rodp.org/students/hardware_software.htm.
Students will also be required to download and install the following
free software packages: Real Player or Windows Media Player, LiveMath
browser plug-in, Peanut WinPlot.
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Instructor Information |
Please see
the separate page inside the course to find instructor contact
information as well as a statement of virtual office hours and other
communication information.
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Assessment and Grading |
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Testing
Procedures:
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Five unit
tests (timed, open book) will be given online. A comprehensive
mid-term exam will be given in a proctored environment. The mid-term
exam will contain a paper-and-pencil only (closed book, no calculator,
no computer) component.
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Grading Procedure:
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Several
quizzes will be administered throughout the semester. These small
quizzes, in most cases, may be attempted an unlimited number of times to
ensure mastery. The quiz average will count 200 points. Homework
problems (usually selected odd problems) will be assigned. Students will
self report percentage completion of homework assignments. The homework
grade will count 100 points. Each test will count 100 points and the
mid-term exam will be 300 points. A participation grade will be assessed
depending on the student's level of participation in online discussions.
A project will be assigned and count 100 points. This represents 1300
total points.
Qz+Hw+T1+T2+T3+T4+T5+ME+PD+PJ
Final Average = -------------------------------
13
Qz = Quiz Average, Hw = Homework
Average , T1 = Test One,
ME = Mid-term Exam, PD = Participation, PJ = Project.
Your progress during the semester may be
calculated by dividing the total points earned to date by the sum of all
possible points to date.
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Grading Scale:
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90 - 100 --- A (1170 -
1300 points)
80 - 89 --- B (1040 - 1169 points)
70 - 79 --- C ( 910 - 1039 points)
60 - 69 --- D ( 780 - 909 points)
0 - 59 --- F ( 0 - 779 points)
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Assignments and Participation |
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Assignments and Projects:
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Homework
will be assigned for each textbook section. These problems will usually
consist of selected odd-numbered problems.
A project
will be assigned related to the student's stated career goal. Students
may work singly or in groups as assigned by the instructor.
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Class
Participation:
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Students
must actively participate in threaded discussion events. Each week the
instructor will begin an organized discussion topic. Students must
respond to these organized discussions as well as contribute to the open
questions and answers posted on the discussion board.
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Punctuality:
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Quizzes,
homework assignments, tests, and the mid-term exam will all have specific
deadlines. These graded activities must be completed by the due date and
time. Make-up work will be accepted only under documented extreme
circumstances.
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Course Ground Rules |
Online math
courses are not for everyone. But for those that approach their online
math course with the correct attitude and diligence, the effort usually
results in a much deeper understanding of the course material than that
acquired in a traditional classroom. My advice would be to establish a
study schedule and stick to it, study the examples online and within the
text, use web resources especially to check answers, and form
study partners or small groups.
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Guidelines for Communications |
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Email:
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- Always
include a subject line.
- Remember
without facial expressions some comments may be taken the wrong way. Be
careful in wording your emails. Use of emoticons might be helpful in
some cases.
- Use
standard fonts.
- Do not
send large attachments without permission.
- Special
formatting such as centering, audio messages, tables, html, etc. should
be avoided unless necessary to complete an assignment or other
communication.
- Respect
the privacy of other class members
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Discussion
Groups:
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- Review
the discussion threads thoroughly before entering the discussion. Be a
lurker then a discussant.
- Try to
maintain threads by using the "Reply" button rather starting a new
topic.
- Do not
make insulting or inflammatory statements to other members of the
discussion group. Be respectful of other’s ideas.
- Be
patient and read the comments of other group members thoroughly before
entering your remarks.
- Be
cooperative with group leaders in completing assigned tasks.
- Be
positive and constructive in group discussions.
- Respond
in a thoughtful and timely manner.
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Chat:
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Introduce yourself to the other learners in the chat session.
- Be
polite. Choose your words carefully. Do not use derogatory statements.
- Be
concise in responding to others in the chat session.
- Be
prepared to open the chat session at the scheduled time.
- Be
constructive in your comments and suggestion
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Web
Resources:
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Library |
The
Tennessee
Virtual Library is available to all students enrolled in the Regents
Degree Program.
Links to library materials (such as electronic journals, databases,
interlibrary loans, digital reserves, dictionaries, encyclopedias, maps,
and librarian support) and Internet resources needed by learners to
complete online assignments and as background reading must be included
in all courses.
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Students With Disabilities
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Qualified
students with disabilities will be provided reasonable and necessary
academic accommodations if determined eligible by the appropriate
disability services staff at their home institution. Prior to granting
disability accommodations in this course, the instructor must receive
written verification of a student's eligibility for specific
accommodations from the disability services staff at the home
institution. It is the student's responsibility to initiate contact with
their home institution's disability services staff and to follow the
established procedures for having the accommodation notice sent to the
instructor.
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Syllabus Changes |
The
instructor reserves the left to make changes as necessary to this
syllabus. If changes are necessitated during the term of the course, the
instructor will immediately notify students of such changes both by
individual email communication and posting both notification and nature
of change(s) on the course bulletin board.
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Technical Support |
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Telephone Support:
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If you are
having problems logging into your course,
timing out of your course, using your course web site tools, or other
technical problems, please contact the AskRODP Help Desk by calling
1-866-550-7637
(toll free)
or go to the AskRODP website at:
http://help.rodp.org
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