MATH 1830
Intuitive Calculus
MWF . . . . . 9:05 – 10:00 am . . . . . Thigpen 115. . . . . SPRING / 2009
https://
elearn.volstate.edu
Mr. Ondis Bible
Associate Professor of Mathematics
http://www2.volstate.edu/OBible
DESCRIPTION:
Limits, continuity, differentiation, integration, and applications. This course will
not substitute for MATH 1910. Intended primarily for business majors.
PREREQUISITE: MATH 1130 with a grade of C or better.
TEXTBOOK:
Calculus for Business, Economics, and the Social and Life Sciences, (9th Ed.),
by Hoffman and Bradley, McGraw-Hill, 2007. Optional Supplementary Text
(Recommended): Student Solutions Manual, Nichols. Copies of this book and
supplement are available for purchase in the VSCC Bookstore or Online.
INSTRUCTOR:
Ondis Bible, Associate Professor of Mathematics, Office Warf-100H, Phone
(615) 230-3386 or ext. 3386 at (615) 741-3215 or (615) 452-8600 or (888) 3358722, FAX (615) 230-3292, Email ondis.bible@volstate.edu Address: VSCC,
1480 Nashville Pike, Gallatin, TN 37066-3188
OFFICE HOURS:
Posted beside office door (W-100H) and on the Internet. Go to
http://www2.volstate.edu/OBible and click on [Office Hours].
GENERAL
EDUCATIONAL
GOAL
The primary educational goal of this course is to provide the student with an
intuitive understanding of differential and integral claculus and its applications to
business and economics.
GENERAL
EDUCATIONAL
OUTCOME
As a result of successfully completing this course, students will have
demonstrated an acceptable level of mastery of the concepts and applications
of an introductory course in calculus.
OTHER
GOALS
This course seeks to provide the necessary techniques of differential and
Integral calculus that students are likely to encounter in undergraduate courses
in business and economics and in their subsequent professional activities.
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OUTCOME
STATEMENTS
Upon completion of this course, the student will have demonstrated an
acceptable ability to:
1. Find the limit of a function, or state that it does not exist.
2. Compute the slope of the secant line through two points on the graph of a given function given the
coordinates of the two points.
3. Use the definition of the derivative to find the derivative of a given function.
4. Write an equation of the tangent line to a curve y = f(x) at a specified value of x.
5. Find the derivative of a polynomial function.
6. Find the derivative of a product of two functions.
7. Find the derivative of a quotient of two functions.
8. Calculate average and instantaneous rate of change.
9. Calculate percentage rate of change.
10. Calculate marginal cost, marginal revenue, and marginal profit.
11. Use the Chain Rule to find the derivative of composite functions.
12. Find the derivative of a power of a differentiable function.
13. Find derivatives by implicit differentiation.
14. Find second and higher-order derivatives of functions.
15. Use the sign of the first derivative to find the intervals over which a function is increasing
ordecreasing and the relative extrema of a function.
16. Use the second derivative to determine the concavity of a curve and to find inflection points.
17. For a given function, find the intervals for which the function is increasing, decreasing, concave
upward, and concave downward. Sketch the graph of the function, showing all relative
extrema and inflection points.
18. Find the absolute maximum and absolute minimum of a given function on a specified interval.
19. Solve application problems in business and economics involving optimization.
20. Solve application problems in elasticity of demand.
21. Sketch the graph of exponential and logarithmic functions.
22. Solve application problems involving exponential and logarithmic models.
23. Find the derivative of exponential and logarithmic functions.
24. Solve application problems involving rates of change of exponential and logarithmic functions.
25. Determine the compound interest from an investment at a given rate if the interest is
compounded a given number of times per year or compounded continuously.
26. Determine the doubling time for a given investment at a given rate if the interest is compounded
a given number of times per year or compounded continuously.
27. Find the effective interest rate if interest is compounded a given number of times per year or
compounded continuously.
28. Find the present value of an investment payable in a given number of years.
29. Determine the compound amount of an investment over a specified period of time with a given
interest rate.
30. Determine the present value of an investment over a specified term with a given interest rate.
31. Find the indefinite integral of a given integrable function.
32. Find an indefinite integral by algebraic substitution.
33. Evaluate the definite integral of a given continuous function on a specified closed interval using
the Fundamental Theorem of Integral Calculus.
34. Use the definite integral to solve application problems in business and economics.
35. Find the area of the region bounded by two given continuous curves on a specified closed
interval.
36. Determine the net excess profit of one investment plan over another given the profit functions of
each.
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37. Determine the net earnings generated by industrial equipment for a specified number of years
given the revenue and cost functions.
38. Define mathematical model and determine the mathematical model for application problems.
39. Define the mathematics of calculus and its two central concepts.
TOPICAL OUTLINE
Functions, Graphs, and Limits
Limits
Differentiation
The Derivative
Techniques of Differentiation
Rate of Change and Marginal Analysis
The Chain Rule
Higher Order Derivatives
Applications of Differentiation
Increase and Decrease; Relative Extrema
Concavity; Curve Sketching
Absolute Maxima and Minima
Practical Optimization Problems
Applications to Business and Economics
Exponential and Logarithmic Functions
Exponential Functions
Exponential Models
The Natural Logarithm
Differentiation of Logarithmic and Exponential Functions
Compound Interest
Integration
Antiderivatives
Integration by Substitution
The Definite Integral
Applications of Integration
Area
Applications to Business and Economics
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ASSESSMENT: The degree to which the primary educational goals of this course have been
achieved will be determined by the cummulative assessment of the course outcomes.
The degree to which this course provides necessary background to pursue other courses can only be
determined by student performance in these other courses. The degree to which the development of
logical thinking and analytical skills is attained is partially assessed by evaluation of homework and
tests but can only be fully assessed by student performance in areas outside this course.
Outcomes statements will be assessed by homework assignments, short quizzes, major tests, and a
comprehensive final examination.
ADA STATEMENT: For students with disabilities:
It is the student’s responsibility to self-identify with the Office of Disability Services to receive
accommodations and services in accordance with The Americans with Disabilities Act (ADA). Only
those students with appropriate documentation and who are registered with the Office of Disability
Services will receive accommodations. For further information, contact the Office of Disability
Services at (615) 230-3472, TDD (615)-230-3488, or visit the office which is located in Room 108,
Wood Campus Center.
EQUAL OPPORTUNITY STATEMENT: Volunteer State Community College is an equal opportunity
Affirmative Action Educational Institution. No person shall be excluded from participation in, be
denied the benefit of, or be subjected to discrimination under any program or activity of the College
because of race, color, national origin, age, or handicap. The college also complies with the Age
Discrimination in Employment Act of 1967, as amended and with the Vietnam Era Veterans'
Readjustment Act of 1974. The commitment to equal opportunity applies to all aspects of
recruitment, employment and education of individuals at all levels throughout the College.
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COURSE POLICIES AND PROCEDURES
WEB-ENHANCED FORMAT: Some components of the course will be administered online. You may
use any computer that has Internet access --- at your home, workplace, or one of the VSCC
computer labs. Go to https://elearn.volstate.edu to enter the course. Your Username is the same as
your VSCC Student Email. Your Password is the same as your Pride Online password.
ATTENDANCE: Prompt and regular attendance is expected. Attendance will be recorded for each
class meeting. Absences in excess of five could result in the student being administratively
withdrawn from the course by the instructor. (See the VSCC Catalog.) Students on financial aid are
reminded that not attending class may result in the requirement that grant money be repaid.
TARDINESS is defined as entering the room after the official starting time for the class. Two
instances of tardiness will count as one absence. It is the responsibility of a student who is tardy, at
the end of the class, to ask the instructor to modify the attendance record. Tardiness is considered
an avoidable class disruption; persistent tardiness will not be tolerated. Any student who already
has two instances of tardiness must get to class on time --- or face the possibility that your
grade will be adversely affected (unless you are late due to an unexpected emergency that can
be documented).
LEAVING CLASS EARLY (before dismissal by the instructor) is permitted in emergency situations.
In non-emergency cases, such as a doctor’s appointment, the student should notify the instructor at
the beginning of class that he/she will be leaving early and should sit close to the door in order to
minimize disruption to the class.
The INCLEMENT WEATHER POLICY for this class is as follows: If VSCC is officially open, this
class will meet as scheduled, all assignments will be due, and any scheduled tests or quizzes will be
given. If VSCC is officially closed, all assignments or tests scheduled for that day are automatically
rescheduled for the next regular class meeting.
If you miss class, or need additional instruction, view the relevant online PowerPoint Presentation
before attempting the homework. If you have technical problems with your computer or the online
components of this course, get the necessary assistance immediately. Call the VSCC Help Desk,
ext. 3367. To log into the online component of the course, go to https://elearn.volstate.edu and log in
to D2L, our online (web-enhanced) course delivery system. Your Username is the same as your
VSCC Student Email. Your Password is the same as your Pride Online password.
CALCULATORS: A scientific calculator is required. A graphing calculator is permitted (nothing
stronger than a TI-84), but not necessary. Hand-held computers and programmable computer-like
calculators (like the TI-89 or TI-92) are not permitted. Sharing a calculator between students is not
permitted on tests or quizzes.
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HOMEWORK: For this course you will do the required Homework online. You are required to
register for MathZone. An access code to MathZone will cost you $25.00 (good for two years).
For instructions on how to register for MathZone, see the MathZone QuickStart Guide attached to
this syllabus. Carefully follow the instructions. You will need a major credit card, an email address,
and the following:
STUDENT SECTION ID:
969-44-DDD
To register and/or Log in to MathZone go to www.mathzone.com . You should save a link to the
MathZone web site to your desktop and/or your browser's "Favorites" folder.
Any student who has not completed the assigned homework before a scheduled quiz or test will be at
a distinct disadvantage, and will be graded more harshly. For those who have completed all relevant
homework by its due date, there will be EXTRA CREDIT available on the next Test. Doing the
assigned homework is absolutely essential for students to learn the skills necessary to successfully
complete this course. Any student who does not successfully complete at least 70% of the relevant
homework may be denied access to a quiz or test and is not eligible for any Extra Credit and/or
Grading Curve that might otherwise be available. For more information on Homework, see
“Homework Assignments” attached to the end of this syllabus. NOTE: Online Mod Checks and
online Discussions are not required in this class.
QUIZZES: All quizzes will be online (multiple choice and/or short answer). Quiz problems must be
worked on paper with answers submitted online to the instructor by the stated deadline. The
textbook, homework, and course notes may be used as a resource when doing a quiz, but
assistance from another person is not permitted. The lowest quiz grade will be dropped.
On the designated quiz date, go to https://elearn.volstate.edu and log in to D2L. Your Username is
the same as your VSCC Student Email. Your Password is the same as your Pride Online password.
A score of zero will be assigned for each quiz not completed and submitted by the stated deadline.
Each student's lowest quiz grade will be dropped. Credit may be given for a late quiz at the
discretion of the instructor, provided the student contacts the instructor in advance to offer a
legitimate explanation and request an extension.
TESTS: There will be four major tests (non-cumulative) and a comprehensive final exam. Students
are required to be present for all on-campus tests. Tests 1, 3, and 4 are online, but Test 2 and the
Final Exam are proctored on campus and will be done on paper. A student who must miss a test due
to an emergency should make every attempt to notify the instructor prior to the time of the test.
Notes, books, and/or assistance from another person are never allowed during a test --- online or
otherwise. Anyone caught CHEATING on a test will receive a grade of zero and may face other
punitive measures.
MAKE-UP TESTS will be given only when the student's absence is due to an unexpected emergency
and is explained by documentation from the appropriate authority (doctor, judge, etc.). Make-up
tests, if allowed, will be harder than the regular test. A score of zero will be assigned for the
missed test if not excused by the instructor. Final exams must be taken at the scheduled time and
will not be returned to the student. There will be no exemptions from taking the Final Exam.
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GRADES: The final numerical grade will be determined according to the following weighted
components.
Tests 1, 3, & 4 = 10% each
Quizzes (lowest dropped) = 15%
Test 2 = 15%
Homework = 10%
Final Exam = 25%
Participation (in class) = 5%
Letter grades will be assigned according to the following numerical grade intervals.
90.00
80.00
70.00
60.00
00.00
-
100 +
89.99
79.99
69.99
59.99
=
=
=
=
=
A
B
C
D
F
Favorable or unfavorable determination of borderline grades will be significantly influenced by
ATTENDANCE and HOMEWORK!
CLASS DISRUPTIONS: An affective mathematics learning environment will enhance (rather than
detract from) a student's (and instructor's) ability to concentrate. Therefore, it is the goal of this
instructor to provide all students with a relaxed, supportive classroom atmosphere free of
unnecessary distractions. Hence, any student who unnecessarily disrupts class (by way of persistent
tardiness, unauthorized talking, and the like) is subject to disciplinary action. Cell phones must be
turned off before coming to class.
CHEATING: Students enrolled in any Volunteer State Community College Course will abide by the
policy regarding academic misconduct found in the Student Handbook at
http://www.volstate.edu/StudentHandbook/conduct.html paying particular attention to section C.(2).
TUTORIAL ASSISTANCE: Trained tutors are available in the Math Lab (Warf 123) or by calling
extension 3387. More information, such as Lab hours are posted on the Math Lab web site at
http://www.volstate.edu/MathScience/Lab/ . A student may contact the instructor during regular office
hours in Warf 100H or by calling (615)741-3215 or (615)452-8600 or 1-888-335-8722, extension
3386. For online interaction with the instructor, use the email component of D2L at
http://elearn.volstate.edu .
MATH 1830 Section V01 Online (Also MATH 1720 and MATH 1910): Students enrolled in the
Online section (V01) of these courses will get their primary instruction by viewing the animated online
PowerPoint presentations. Students enrolled in a traditional lecture section are encouraged to view
these presentations as needed for additional tutorial assistance. This may be done anywhere the
student has access to a personal computer linked to the Internet, including those in VSCC computer
labs. You may view any of these online presentations at http://www2.volstate.edu/obible .
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HOMEWORK ASSIGNMENTS
MATH 1830 – Intuitive Calculus
TEXTBOOK: Calculus for Business, Economics, and the Social and Life Sciences, (9th Ed.), by
Hoffman and Bradley. Optional Supplementary Text : Student Solutions Manual, Nichols.
Doing only the assigned homework may not constitute adequate practice for some students to learn
the required skills. Some students may need to attempt additional problems.
Read your syllabus (before the second class meeting). Study the course policies in "Policies and
Procedures" and abide by them. Any questions or misunderstandings concerning these policies
should be cleared up as soon as possible.
Reviews: Do the Review assignments on paper (no MathZone submission). Doing the Review is
not required, but it is highly recommended that you do these exercises to prepare for the next Test.
LSN SECTION
PAGE
EXERCISES
1
1.5
P69
Homework 01 (in MathZone)
2
2.1
P108
Homework 02 (in MathZone)
3
2.2
P121
Homework 03 (in MathZone)
Quiz 1 (1.5, 2.1, 2.2)
4
2.3
P134
Homework 04 (in MathZone)
5
2.4
P147
Homework 05 (in MathZone)
P70
P89
P177
16, 26
30 – 33
1 – 15, 18a, 18b, 19a, 20a, 20b, 21a, 21b,
22a, 22c, 30, 32, 56
Quiz 2 (2.3, 2.4)
Review 1
(Count = 33)
Test 1 (1.5, 2.1 – 2.4)
6
3.1
P198
Homework 06 (in MathZone)
7
3.2
P216
Homework 07 (in MathZone)
Quiz 3 (3.1, 3.2)
8
3.4
P249
Homework 08 (in MathZone)
9
3.5
P265
Homework 09 (in MathZone)
P273
1-7, 11, 13, 21 – 23, 25 – 27, 31, 32, 37,
40, 42 - 46
Quiz 4 (3.4, 3.5)
Review 2
(Count = 24)
Test 2 (3.1, 3.2, 3.4, 3.5)
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LSN SECTION
PAGE
EXERCISES
10
4.1
P298
Homework 10 (in MathZone)
11
4.2
P314
Homework 11 (in MathZone)
Quiz 5 (4.1, 4.2)
12
4.3
P330
Homework 12 (in MathZone)
13
4.4
P341
Homework 13 (in MathZone)
P350
6abcd, 7 – 10, 14 – 18, 46 – 48, 50 – 52,
56 – 59
Quiz 6 (4.3, 4.4)
Review 3
(Count = 20)
Test 3 (4.1 – 4.4)
14
5.1
P371
Homework 14 (in MathZone)
15
5.2
P383
Homework 15 (in MathZone)
Quiz 7 (5.1, 5.2)
16
5.3
P399
Homework 16 (in MathZone)
17
5.4
P416
Homework 17 (in MathZone)
P452
1, 2, 7, 9 – 14, 16, 21, 25, 27, 30, 31, 35 – 37,
59, 65, 68, 69, 87
Quiz 8 (5.3, 5.4)
Review 4
(Count = 23)
Test 4 (5.1 – 5.4)
Final Review (NOT to be turned in)
Also study your Tests (1 - 4)and Quizzes (1 - 8).
Final Exam
(Comprehensive)