MATH 110 - Techniques of Calculus I
Penn State University
Spring Semester 2014
Dr. James Hager
Office: 211 McAllister Building
Phone: 863 – 8753
email: jah14@psu.edu
Office Hours: TTH: 1:00-3:00
and By Appointment
Textbook: Applied Calculus for the Managerial, Life, and Social
Sciences, 9th Edition, by S.T. Tan, available in textbook, hybrid
textbook, or eBook formats. All versions are acceptable for this class.
The easiest way to purchase your textbook is to navigate to the
www.cengagebrain.com/micro/PSUmath110 website and purchase either
the hybrid textbook ($112) with EWA or the e-book ($65). Do not purchase
both! You may also go to the PSU bookstore and purchase the printtextbook or eBook. All new 9th edition S. T. Tan textbooks or eBooks come
bundled with the WebAssign learning environment. If you choose to
purchase a used copy of the textbook, you may purchase the WebAssign
learning environment directly from the WebAssign website at an additional
cost. The WebAssign materials include: 1) a significant number of
homework/exercise problems from the chapters covered during the lectures,
2) instructional videos, and 3) step-by-step tutorials. Access to these
materials is granted by the license/key included in your
textbook/eBook. Although the completion of WebAssign exercises will not
be used directly in the calculation of your grades, students are highly
encouraged to explore these materials. Based on the usefulness of these
learning aids, a goal during the semester is to integrate some of these
materials into the classroom lecture discussions.
Course Description
TECHNIQUES OF CALCULUS I (4) Functions, graphs, derivatives,
integrals, techniques of differentiation and integration, exponentials,
improper integrals, applications. Students may take only one course for
credit from MATH 110, 140, 140A, and 140B. Prerequisite: MATH 022 or
satisfactory performance on the mathematics proficiency examination
Course Coverage
The goal for the course is to cover Chapters 2-6 from the text. Chapter 1 is
considered review material for the students. Each student should confirm
that they understand the material in Chapter 1 during the first week of the
course.
Exams
Two evening examinations (midterms) will be given. The dates and times of
these exams will be as follows:
Examination 1: Monday, March 3, 2013 6:30 - 7:45 pm
Examination 2: Tuesday, April 8, 2013 6:30 - 7:45 pm
Information on the locations and content of these exams will be distributed
at a future date.
Conflict/Makeup Exams
In addition to the regularly scheduled exam, the math department schedules
two additional options: a conflict exam for each of the midterms from 5:05 6:20 on the same night as the regularly scheduled exam and a makeup exam
scheduled on an evening different from the regularly scheduled exam night.
Students who attend the conflict exam will not be permitted to leave before
6:25. Sign-up sheets for both the conflict exam and the makeup exam will be
distributed by your instructor during class. If you need to schedule the
conflict exam, you must sign up at least one full week ahead of the
scheduled exam date. A valid conflict/makeup reason is required to sign up
for either of these exams.
NOTE: If you miss an exam without an official excuse (such as illness or
official university business), then you may be allowed to take a makeup
exam, but with an automatic 25% deduction from the grade. To avoid
this deduction, you must notify your lecturer, with your official excuse,
before the date and time of the exam. This notification may be
performed in person, via e-mail, or by telephone.
Final Exam
The final examination in the course will be comprehensive. It will be given
during the university's final examination week, May 5-9, 2014. Do not make
plans to leave the university before the end of this week. Travel plans do not
constitute an official university excuse for missing an examination or for
obtaining a conflict or makeup examination. Conflicts for the final exam are
determined by scheduling - any student with a potential final exam conflict
situation should apply online before the final exam conflict application
period expires. The math department does not offer a makeup exam option
for the final exam.
Readiness Test
A Readiness Test is posted under your Lessons tab in your Angel Math 110
workspace. Since the purpose of the Readiness Test is to test the basic
algebraic skills required to be successful in Math 110, it is critical that
everyone take the test during the first week of classes. The results of the
Readiness Test will not be used in any way during the calculation of your
overall course grade. Students who score poorly on this test should work the
Chapter 1 self-assessment exercises also included on Angel and, if still
finding difficulty with the preparatory materials, strongly consider taking
Math 22 before proceeding with Business Calculus. Minimally, all students
should review the basic algebraic concepts covered by the test questions
during the first week of the semester in preparation for the related Calculus
materials. Chapter 1 of your textbook also provides background materials
that may be helpful in preparation for the Calculus concepts discussed in
Chapters 2 - 6.
In-Class Quizzes
Several short quizzes will be given throughout the course of the semester
during the recitation class. The quiz questions will be similar to the assigned
homework problems and the reading done in preparation for class. The
purpose of the quizzes is to encourage you to keep up with your preparation
(and reward you for doing so). Each quiz will consist of problems based on
the materials presented during the previous week's lectures.
Twelve quizzes are planned for the semester. A student's quiz grade will be
determined by summing each student's highest ten quiz scores and dropping
the remaining ones. Each quiz will be worth 10 points.
Only students with documented university-approved absences will be
allowed to makeup missed quizzes (e.g. university sports - participation,
health/injury. etc.). Students need to contact their recitation leaders (not their
lecturers) to discuss any issues related to quiz policies. The quiz content,
specific makeup policies, partial credit rubric, etc. are all determined by your
individual recitation leader.
Self-Assessment Tests
Self Assessment Tests are posted under the Lessons tab at your Math 110
Angel website. The Self Assessment Tests provide additional
problems/examples that allow you to further explore the key concepts
introduced in the lecture classes and assigned homework problems. After
submitting the tests, a numerical score is calculated and feedback provided
on the correct approach for solving each problem. Each instance of the Self
Assessment Test is unique, so you may take these tests several times and
still benefit from working through the problems. Similar to homework
problems, calculators may be useful to fully explore the problem solutions.
Although the self-assessment tests are scored, their purpose is mainly selfdiagnostic - the numerical results are not included in the determination of
your course grades.
Example Practice Exams
Models of previous Math 110 exams are included in a folder under the
Lessons tab in your Math 110 Angel website. Care should be taken in the
usage of these models during the preparation for each exam, i.e., students
should understand that the exams for this semester are not based strictly on
the practice exams. Good study/preparation habits include the review of
lecture notes, completion of assigned homework problems, completion of
self-assessment exercises, and where appropriate, attendance at
supplemental instruction help sessions. Your lecturer will provide specific
guidance prior to each exam on the specific topics included/excluded.
Suggested Homework
A list of suggested homework problems appears at the end of this syllabus.
These homework problems will not be turned in for a grade. The purpose of
doing the homework is to better understand the material discussed in the
lectures and to prepare oneself for the quizzes and exams. Since much of this
material builds upon previous material, you are encouraged to complete
many of the suggested homework and keep up with the suggested
homework, even though it will not be collected. Solutions to the suggested
homework problems are posted in a folder under your Angel Lessons Tab.
Academic Integrity
Academic integrity is the pursuit of scholarly activity in an open, honest and
responsible manner. Academic integrity is a basic guiding principle for all
academic activity at The Pennsylvania State University, and all members of
the University community are expected to act in accordance with this
principle. Consistent with this expectation, the University's Code of Conduct
states that all students should act with personal integrity, respect other
students' dignity, rights and property, and help create and maintain an
environment in which all can succeed through the fruits of their efforts.
Academic integrity includes a commitment not to engage in or tolerate acts
of falsification, misrepresentation or deception. Such acts of dishonesty
violate the fundamental ethical principles of the University community and
compromise the worth of work completed by others.
Based on the University's Faculty Senate Policy 49-20, a range of academic
sanctions may be taken against a student who engages in academic
dishonesty. Please see the Eberly College of Science Academic Integrity
homepage for additional information and procedures.
Disability Services
Penn State welcomes students with disabilities into the University's
educational programs. Every Penn State campus has an office for students
with disabilities. The Office for Disability Services (ODS) Web site provides
contact information for every Penn State campus:
http://equity.psu.edu/ods/dcl. For further information, please visit the Office
for Disability Services Web site: http://equity.psu.edu/ods.
In order to receive consideration for reasonable accommodations, you must
contact the appropriate disability services office at the campus where you are
officially enrolled, participate in an intake interview, and provide
documentation: http://equity.psu.edu/ods/doc-guidelines. If the
documentation supports your request for reasonable accommodations, your
campus’s disability services office will provide you with an accommodation
letter. Please share this letter with your instructors and discuss the
accommodations with them as early in your courses as possible. You must
follow this process for every semester that you request accommodations.
Grading
Your course grade will be determined by your exam scores and your quiz
scores.
Total possible points follow:
Examination I
Examination II
Quizzes
Final Examination
Total
100
100
100
150
450
The exact point requirements for each letter grade will be decided at the
end of the course. General University guidelines follow:
Grade %-Score
Points
A
93 - 100
417 - 450
A-
90 - 92
403 - 416
B+
87 - 89
390 - 402
B
83 - 86
372 - 389
B-
80 - 82
358 - 371
C+
77 - 79
345 - 357
C
70 - 76
313 - 344
D
60 - 69
268 - 312
F
0 - 59
0 - 267
After the second exam and before the late-drop deadline, if required, the
grade-line cutoffs for the major grades (A, B, C, D, F) will be updated to
facilitate your planning for the remainder of the semester. The +/- gradelines will be assigned after the final exam. The unavoidable consequence is
that some students are just a point away from a higher grade. For reasons of
fairness, the policy in this course is to NOT adjust individual grades in such
circumstances.
Note: Your grade will be based exclusively on the midterm examinations,
final examination, and quiz scores. There is no extra credit work. Students
are encouraged to discuss their performance with their lecturers and
recitation leaders regularly during the semester, and if appropriate, work out
strategies to improve overall study, problem solving, and knowledge
retention skills.
Deferred Grades: Students who are unable to complete the course because
of illness or emergency may be granted a deferred grade, which will allow
the student to complete the course within the first six weeks of the following
semester. Note that deferred grades are limited to those students who can
verify and document a valid reason for not being able to take the final
examination. For more information, see DF grade.
Class Attendance
Although regular classroom attendance will not be used to determine your
grade in a tangible way, you are strongly encouraged to regularly attend
class. Attending classes is beneficial to your understanding of the materials
described in the text. Seeing the material presented in a lecture is extremely
helpful as the presentation will often be different than the text in order to
clarify and enhance the reading assignments. Additionally, material not
present in the text may be presented in class; you will be held accountable
for this material on quizzes and exams.
Classroom Protocol
Please turn off all cell phones and put away all materials not directly related
to the course (e.g. newspapers). Since noises are greatly amplified in the
lecture halls, it is important that non-essential conversations are minimized.
Finally, if you must leave early, please notify your lecturer at the beginning
of class and sit near an exit to minimize classroom disturbance.
Calculator Usage
A graphics-business calculator is highly recommended, but any calculator
that can compute "x to the power y" is sufficient. It may be used, as
appropriate, in the lectures, self-assessment tests, and homework, but will
not be allowed on the in-class quizzes, two midterms and final examination.
Obtaining Assistance
There are various avenues for obtaining assistance for this course:
•
•
•
•
Your lecturer - office hours appear above
Your recitation instructor - they will also hold office hours each week
The Math Tutoring Center (part of Penn State Learning located on the
2nd floor Boucke building)
Guided Study Group (part of Penn State Learning - Times TBA
later)
Hopefully Helpful Hints
o
o
o
o
Learn for the long term. Strive to retain the knowledge that
you acquire. Do not simply try to learn material a couple of
days before an exam with the goal of forgetting it right after
finals. View the learning of the material as an active
process, not a passive one. (You are here to learn, not to
receive grades.) Learning is a process, not an event.
Strive to know the material, to understand it at a very deep
level, rather than a superficial one.
Do the homework with as little help (solutions manuals,
friends, etc.) as possible. Balance the use of group learning
with individual study so you actually know the material.
Ask questions, either in class or during office hours.
o
o
o
o
o
o
Read the textbook before the planned lecture. The tentative
schedule of classes gives you a guide as to what to read in
advance.
Carefully study and rework the examples in the text.
Re-read and rewrite your notes.
Study for exams progressively, over a long period of time.
Begin the studying process at least one week prior to the
date of the exam.
Manage your time wisely. Plan to spend at least two hours
outside of class for every hour in class, if not more!
Take responsibility for your education. Work the selfassessment tests and learn from the objective feedback.
Final Comments
It is our hope that your appreciation for mathematics will grow during this
semester. Although the applications we cover are limited in scope, the
application of mathematics extends to many areas in your chosen careers.
The Calculus skills developed in this class provide a solid foundation for
addressing many of the questions that surface during the introduction of
standard business models in your future coursework.
Tentative Class Schedule (Lectures)
Day
Date
Material Covered
Other Information
M
1/13
Course Overview
First Day of Classes
W
1/15
2.1
F
1/17
2.2
M
1/20
W
1/22
2.3
F
1/24
2.3, 2.4
M
1/27
2.4, 2.5
MLK Day
No Classes
Regular Drop Deadline
W
1/29
2.5
F
1/31
2.6
M
2/3
3.1
W
2/5
3.2
F
2/7
3.3
M
2/10
3.4
No Intermediate Value Theorem
Applications
•
•
•
•
W
2/12
3.4
F
2/14
3.5
M
2/17
3.6
•
Marginal Revenue, Cost, Profit
Marginal Average Revenue,
Cost, Profit
Elasticity
Elasticity and Revenue
Related Rates - Basic
Algebraic/Geometric
Applications
Related Rates - Business
Applications
W
2/19
3.6
F
2/21
4.1
M
2/24
4.2
W
2/26
4.2
Starts Exam 2 Material
Application of Second Derivative
•
F
2/28
4.3
M
3/3
4.4
Law of Diminishing Returns (not
discussed in textbook)
Exam 1 – Monday Mar 3
6:30-7:45
Room Assignments Posted under Angel
- Lessons tab
W
3/5
4.5
•
•
Absolute Extrema
Optimization - Business
Applications
F
3/7
4.5
•
Optimization - Basic Algebraic /
Geometric Applications
Optimization - More Advanced
Business Applications
•
Spring Break
March 9-15
M
3/17
5.1
W
3/19
5.2
F
3/21
5.3
M
3/24
5.3
W
3/26
5.4
F
3/28
5.4
M
3/31
5.5
W
4/2
5.5
F
4/4
6.1
M
4/7
6.1
•
•
•
•
Compound Interest
Continuous Interest
Effective Rates of Interest
Present Value
Starts Materials for the Final Exam
Exam 2
Tuesday, April 8
6:30-7:45
Room Assignments Posted under Angel
- Lessons tab
W
4/9
6.2
F
4/11
6.2
M
4/14
6.3
W
4/16
6.4
F
4/18
6.5
M
4/21
6.5, 6.6
W
4/23
6.6
F
4/25
6.7
Late Drop Deadline
•
•
•
M
4/28
6.7
W
4/30
6.7
F
5/2
6.7
Consumer / Producer Surplus
Future/Present Value of
Continuous Income Stream
Annuity Amount and Present
Value
Last Day of Classes
Final Exams
May 5 - 9
Suggested Homework Problems
Section Problems
2.1
1-13 odd, 23-34, 39-50, 51-58
2.2
1-23 odd, 25-34, 43-52, 64, 65, 66
2.3
1-7 odd, 9-14, 17, 18, 51, 53, 55, 66-69, 72, 73 76
2.4
1-8, 17-22, 23-39 odd, 49-66, 73-80, 83
2.5
1-14, 15-20, 21-35, 39-44, 45-55, 57-60, 73, 74
2.6
9-21, 23, 24, 34, 35, 47-52
3.1
1-36, 37, 38, 41-46, 67
3.2
1-29, 35-41, 46, 48, 56
3.3
1-53 odd, 61-64, 85
3.4
3-17, 23-33
3.5
1-19 odd
3.6
1-8, 9-29 odd, 41-47
4.1
11, 12, 13-35 odd, 37-43, 45-48, 49-65 odd
4.2
1-8, 11-14, 25-59 odd, 61-75 odd, 94
4.3
1-10, 11-27 odd, 37-57 odd, 62
4.4
1-8, 9-27 odd, 40, 45-47
4.5
5, 8, 9, 10, 17
5.1
1-18 odd, 17-26
5.2
1-11 odd, 17-20, 21-28, 35-42
5.3
1-28
5.4
1-28, 33-40, 43-46, 63, 67
5.5
1-33 odd, 41-50, 51-58
6.1
9-48, 51-58, 67-70
6.2
1-46 odd, 59
6.3
3, 5, 7, 13, 15
6.4
5-16, 17-40, 41, 42, 43
6.5
1-27, 29-41 odd, 57, 61
6.6
1-16, 17-33 odd
6.7
1-18, 22
Learning Objectives
Upon successful completion of Math 110, the student should be able to:
1.
Identify polynomial, rational, power, exponential, and
logarithmic functions.
2.
Calculate the domains of polynomial, rational, power,
exponential, and logarithmic functions.
3.
Calculate the sums, differences, products, quotients, and
compositions of functions.
4.
Model cost, revenue, profit, supply, and demand business
functions.
5.
Calculate equilibrium points within supply/demand markets
and interpret the results.
6.
Calculate or estimate finite/infinite limits of functions given by
formulas, graphs, or tables.
7.
Calculate one-sided limits of functions.
8.
Determine whether a function given by a graph or formula is
continuous at a given point or on a given interval.
9.
Determine whether a function given by a graph or formula is
differentiable at a given point or on a given interval.
10. Distinguish between average and instantaneous rate of change
and interpret the definition of the derivative graphically.
11. Determine derivatives of some functions using the definition of
derivative of a function.
12. Calculate derivatives of polynomial, rational, power,
exponential, and logarithmic functions, and combinations of these
functions.
13. Calculate derivatives of implicitly defined functions.
14. Apply the ideas and techniques of derivatives to related rate
problems to include basic algebraic/geometric models and
cost/average cost, revenue/average revenue, profit/average profit,
supply, and demand models
15. Apply the ideas and techniques of derivatives to perform
marginal analysis of basic economics models.
16. Apply the ideas and techniques of derivatives to calculate
elasticity of basic economics models.
17. Apply the ideas and techniques of derivatives to determine
intervals where a models/graph is:
(a) Increasing/decreasing
(b) Concave up/down
18. Apply the ideas and techniques of derivatives to determine points
in a model/graph that are:
(a) Relative extrema
(b) Absolute extrema
(c) Critical
(d) Inflection
19. Identify vertical and horizontal asymptotes
20. Apply the ideas and techniques of derivatives to graphing or
recognizing the graphs of functions.
21. Apply the ideas and techniques of derivatives to optimization
problems to include basic algebraic/geometric models and cost,
revenue, profit, supply, and demand models.
22. Apply the ideas and techniques of derivatives to solve:
(a) Compound interest
(b) Continuous interest
(c) Effective interest rate
(d) Present value
business models.
23. Determine the point-of-diminishing returns for a model/function.
24. Calculate the derivatives of functions using logarithmic
differentiation
25. Calculate the Riemann sum for a given function, partition and
collection of evaluation points.
26. Describe a definite integral as the limit of a Riemann sum.
27. Determine anti-derivatives of basic algebraic functions.
28. Calculate values of definite integrals using anti-derivatives and
areas.
29. Apply concepts of integration to solving basic business model
applications
30. Apply substitution techniques to integrate basic functions.
31. Apply the ideas of definite integrals to solve problems of areas.
32. Calculate the average value of business models using the definite
integral.
33. Apply the ideas and techniques of the definite integral to
evaluate:
(a) Consumer/producer surplus
(b) Future/present value of income streams
(c) Future/present value of annuities
business models.
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