MATH 1830
Intuitive Calculus
MWF . . . . . 9:05 – 10:00 am . . . . . ROOM W104 . . . . . SPRING / 2006
http://
vswebct.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, (8th Ed.),
by Hoffman and Bradley. 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: Basic Concepts
The Derivative
Techniques of Differentiation
Product and Quotient Rules; Higher-Order Derivatives
The Chain Rule
Applications of the Derivative
Increasing and Decreasing Functions; Relative Extrema
Concavity and Points of Inflection
Curve Sketching
Optimization
Exponential and Logarithmic Functions
Exponential Functions
Logarithmic Functions
Differentation of Logarithmic and Exponential Functions
Exponential Models
Integration
Antidifferentiation: The Indefinite Integral
Integration by Substitution
The Definite Integral and the Fundamental Theorem of Calculus
Applying Definite Integration: Area Between Curves
Applications to Business and Economics
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.
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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 will receive services. For further information, contact
the Office of Disability Services at X3472 or visit the office which is located on the ground floor of the
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
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.
CALCULATORS: A scientific calculator is required. A graphing calculator is permitted, but not
necessary. Sharing a calculator between students is not permitted on tests or quizzes. Hand-held
computers and programmable computer-like calculators (like the TI-89 or TI-92) are not permitted.
HOMEWORK: Assigned homework must be completed (in pencil, not ink, except homework to be
faxed) before coming to class. Textbook pages and sections must be properly labeled, and problems
must be correctly numbered with answers highlighted, boxed, circled, or underlined. Work must be
shown where work is necessary. In most cases, no credit will be given for answers without the
proper steps shown. At the top of the first page must also be written (as a fraction) the number of
problems completed over the number of problems assigned in that lesson. Inaccurate reporting of
this homework grade may be penalized. Randomly selected problems will be graded.
Each student is allowed a maximum of three late assignments without direct penalty. After three, late
homework (not handed in when instructed) will receive half credit, provided it is turned in within one
week after the due date. A homework assignment handed in late due to an absence is still
considered late. Homework may be handed in early when an absence is expected. 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.
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Warning: 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.
QUIZZES: All scheduled 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.
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 an
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 scheduled tests. 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. 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 significantly harder than the regular test. A score of zero will be
assigned for the missed test if the absence is 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. Specifics of Extra Credit on the Final Exam will be announced near the
end of the semester.
GRADES: The major test grades, the final exam grade, the quiz grades, and the homework grade
will be averaged to obtain the final numerical grade. These grades will count in the final average as
follows:
Tests = 60%
Exam = 15%
Quizzes = 15%
Homework = 10%
Letter grades will be assigned according to the following 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!
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EXTRA CREDIT – Online Participation (Optional):
In the first week of the semester, go to http://vswebct.volstate.edu and log in to the course in
WebCT, our online (web-enhanced) course delivery system. Your WebCT ID is the same as
your VSCC Student Username (used for Student Email). Your username is typically your first
initial and last name with no spaces between (e.g. jsmith). If you do not know your Username,
you can look it it up http://www.volstate.edu/studentemail/lookup/lookup.asp . Your Password
is your six-digit birth date (mmddyy).
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. 3302.
Quik Cheks: These online “mini-quizzes” will count as homework points (extra credit), and
will consist of seventeen problems, one for each of the seventeen lessons, to be done online
after completing the assigned homework for that lesson. Doing these extra credit Quik Cheks
can add as much as 4% to your Homework Average.
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: A student may get additional tutorial assistance from the instructor
during regular office hours in W-100H or by calling (615)741-3215 or (615)452-8600 or 1-888-3358722, extension 3386. For online interaction with the instructor, use the email component of WebCT.
Trained tutors are also available in the Math Lab (W-125) or by calling extension 3387. Lab hours
are posted on the Math Lab web site at http://www.volstate.edu/MathScience/Lab/.
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, (8th Ed.), by
Hoffman and Bradley. Optional Supplementary Text (Recommended): Student Solutions Manual,
Nichols.
Doing only the assigned homework may not constitute adequate practice for some students to learn
the required skills. Students should attempt additional problems (not to be handed in) until complete
mastery is attained.
To receive credit, homework, quizzes, tests, and the final examination must be neat, orderly, in
proper notation, written precisely, and must be written in pencil. (Any student work that is to be faxed
or scanned should be written in black, erasable ink.) All graphs must be done on graph paper (or
copy paper, if done and printed from a graphing utility).
LSN
SECTION
PAGE
EXERCISES
COUNT
1
1.5
P68
1 – 8, 13, 15, 16, 21, 23 – 26
17
2
2.1
P106
1 – 6, 9, 11, 12, 17, 21 – 23, 25, 33
15
3
2.2
P118
1, 5, 11 – 14, 17, 21, 26, 35, 39, 45, 46, 55, 61,
65, 66, 68, 69
19
Quiz 1 (1.5, 1.6, 2.1, 2.2)
4
2.3
P131
1, 3, 7, 9, 11, 23, 29, 38, 40, 43, 51, 52, 57,
58, 61
15
5
2.4
P143
1, 3, 7, 13, 19, 23, 26, 27, 29, 31, 40, 41, 49, 55,
56, 59, 64
17
P69
P87
P172
16, 26
30 – 33
1 – 15, 18a, 18b, 19a, 20a, 20b, 21a, 21b, 22a,
22c, 30, 32, 56
33
Quiz 2 (2.3, 2.4)
REVIEW 1
TEST 1 (1.5, 2.1 – 2.4)
6
3.1
P194
1 – 5, 8, 11, 13, 23, 26, 33, 41, 43, 45, 49, 55, 57
17
7
3.2
P212
1, 2, 5, 8, 13, 15, 17, 19, 27, 28, 33, 35, 40, 55, 57
15
P244
1, 2, 4, 5, 7, 17, 19, 23, 25, 27, 29, 33, 41
13
Quiz 3 (3.1, 3.2)
8
3.4
9
LSN
SECTION
PAGE
EXERCISES
COUNT
9
3.5
P260
1, 3, 5, 7, 9, 15, 18, 27, 28, 30, 31
11
P268
1-7, 11, 13, 17 – 19, 21 – 23, 27, 28, 33, 34,
36 - 39, 42
24
Quiz 4 (3.4, 3.5)
REVIEW 2
TEST 2 (3.1, 3.2, 3.4, 3.5)
10
4.1
P292
1, 5, 8 – 10, 13, 19, 27, 29, 33, 42, 49, 55, 56
14
11
4.2
P308
1, 3 – 9, 13, 21 – 23, 26 – 29, 33, 35, 36, 39,
26
41 – 43, 48, 54, 59
Quiz 5 (4.1, 4.2)
12
4.3
P322
1, 3, 5, 7, 9, 11, 13 – 15, 17, 19, 20, 36, 39, 41,
59, 61, 63, 69
19
13
4.4
P334
7, 9, 21, 22, 26 – 28, 30, 35, 37, 44
11
P343
6abcd, 7 – 10, 14 – 18, 46 – 48, 50 – 52, 56 – 59
20
Quiz 6 (4.3, 4.4)
REVIEW 3
TEST 3 (4.1 – 4.4)
14
5.1
P365
1 – 3, 5, 11 – 13, 15, 19, 21, 23, 24, 31, 32, 35,
41, 45
17
15
5.2
P377
1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23 – 28
17
P393
11, 13, 15, 17, 19, 21, 23, 25, 27, 31 – 34, 37,
22
Quiz 7 (5.1, 5.2)
16
5.3
39, 40, 43, 47, 48, 51, 57, 62
17
5.4
P509
3, 5, 8, 9, 11, 12, 14, 40, 44
P438
1, 2, 7, 9 – 14, 16, 21, 25, 27, 30, 31, 35 – 37,
51, 57, 60, 61, 79
9
Quiz 8 (5.3, 5.4)
REVIEW 4
TEST 4 (5.1 – 5.4)
Final Review
Final Exam (Comprehensive)
23