MATH 110 - Techniques of Calculus I
Penn State University
Fall Semester 2012
Dr. James Hager - Coordinator
Dr. Ping Xu
Office: 211 McAllister Building
Office: 329 McAllister Building
Phone: 863 – 8753
Phone: 865 – 3517
email: hager@math.psu.edu, jah14@psu.edu
email: ping@math.psu.edu
Office Hours: TTH: 1:00-3:00
and By Appointment
Office Hours: MW: 2:30-3:30
Textbook: Applied Calculus for the Managerial, Life, and Social
Sciences, 8th Edition, by S.T. Tan (Brooks/Cole), e-textbook or
textbook.
In addition to the option of purchasing your textbook from the bookstore, if
you navigate to the cengagebrain.com website, there are a variety of
alternative ways / formats for acquiring the textbook materials including:
renting your textbook, purchasing e-textbooks, or purchasing individual echapters. If you plan to take Math 111, you will not need to purchase an
additional textbook - the same textbook will support both classes. All new S.
T. Tan 8th edition copies of your textbook sold in the Penn State Bookstore
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. 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: Wednesday, October 3, 2012 6:30 - 7:45 pm
Examination 2: Wednesday, November 7, 2012 6:30 - 7:45 pm
Information on the locations 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, December 17-21, 2012. 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.
In addition, a Collaboration tab is included for you to post questions and
responses related to the content/solutions of these problems to the rest of the
class. Where helpful, I will periodically review these postings and provide
additional guidance where necessary.
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.
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, A-
90-100
405-450
B+, B, B- 80-89
360-404
C+, C
70-79
315-359
D
60-69
270-314
F
0-59
0-269
After the second exam and before the late-drop deadline, the grade-line
cutoffs for the major grades (A, B, C, D, F) will be provided to facilitate
your planning for the remainder of the semester. The +/- grade-lines 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)
JAVA Applets
The following link www.math.psu.edu/dlittle/java/calculus/index.html
provides a set of JAVA utilities that may be helpful in exploring some of the
content introduced in this course.
Hopefully Helpful Hints
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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.
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 self
assessment 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
8/27
Course Overview
First Day of Classes
W
8/29
2.1
F
8/31
2.2
M
9/3
W
9/5
2.3
F
9/7
2.3, 2.4
M
9/10
2.4, 2.5
W
9/12
2.5
F
9/14
2.6
M
9/17
3.1
W
9/19
3.2
F
9/21
3.3
M
9/24
3.4
Labor Day – No Classes
No Intermediate Value Theorem
Applications
•
•
•
•
Marginal Revenue, Cost, Profit
Marginal Average Revenue,
Cost, Profit
Elasticity
Elasticity and Revenue
W
9/26
3.4
F
9/28
3.5
•
•
M
10/1
3.5, 3.6
W
10/3
4.1
•
Related Rates - Basic
Algebraic/Geometric
Applications
Related Rates - Business
Applications
Related Rates – Business
Applications
Starts Exam 2 Material
Exam 1 – Wednesday Oct 3
6:30-7:45
Room Assignments Posted under Angel
- Lessons tab
F
10/5
4.1
M
10/8
4.2
W
10/10
4.2
Application of Second Derivative
•
Law of Diminishing Returns (not
discussed in textbook)
F
10/12
4.3
M
10/15
4.4
W
10/17
4.5
•
•
Absolute Extrema
Optimization - Business
Applications
F
10/19
4.5
•
Optimization - Basic Algebraic /
Geometric Applications
Optimization - More Advanced
•
Business Applications
M
10/22
5.1
W
10/24
5.2
F
10/26
5.3
M
10/29
5.3
W
10/31
5.4
F
11/2
5.4
M
11/5
5.5
W
11/7
5.5
•
•
•
•
Compound Interest
Continuous Interest
Effective Rates of Interest
Present Value
Exam 2
Wednesday, November 7
6:30-7:45
Room Assignments Posted under Angel
- Lessons tab
F
11/9
6.1
M
11/12
6.1
W
11/14
6.2
F
11/16
6.2
Late Drop Deadline
Thanksgiving Holiday
No Classes
November 18-24
M
11/26
6.3
W
11/28
6.4
F
11/30
6.5
M
12/3
6.5, 6.6
W
12/5
6.6
F
12/7
6.7
•
•
•
M
12/10
6.7
W
12/12
6.7
F
12/14
6.7
Consumer / Producer Surplus
Future/Present Value of
Continuous Income Stream
Annuity Amount and Present
Value
Last Day of Classes
Suggested Homework Problems
Section Problems
1.1
1-53 odd, 63-74, 75-89 odd
1.2
1-6, 7-23 odd, 25-36, 41-57 odd, 59-63
1.3
1-33 odd
1.4
1-10, 11-45 odd
2.1
1-13 odd, 23-33, 39-58
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, 74, 75, 78
2.4
1-8, 17-22, 23-39 odd, 49-66, 73-80, 83
2.5
1-14, 21-35, 39-44, 45-55, 57-60
2.6
9-21 odd, 23, 24, 34, 35, 47-52
3.1
1-38, 41-46
3.2
1-29, 35-41, 46, 48
3.3
1-53 odd, 61-64
3.4
3-17 odd, 23-33
3.5
1-19 odd
3.6
1-8, 9-29 odd, 41-47
4.1
13-35 odd, 37-43, 45-48, 49-65 odd
4.2
1-8, 11-14, 23-65 odd, 90
4.3
1-10, 11-27 odd, 37-43, 49-53, 56, 62
4.4
1-8, 9-27 odd, 40, 46-53
4.5
5, 8, 9, 10, 17
5.1
1-25 odd
5.2
17-20, 21-28, 35-42
5.3
1-28
5.4
1-28, 33-39, 43-46, 62, 63
5.5
1-33 odd, 41-50, 51-58
6.1
9-50, 51-58, 67-70
6.2
1-43 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, 56, 59
6.6
1-16, 17-33 odd
6.7
1-18
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 finding extrema.
18. Apply the ideas and techniques of derivatives to graphing
functions.
19. Apply the ideas and techniques of derivatives to optimization
problems to include basic algebraic/geometric models and cost,
revenue, profit, supply, and demand models.
20. Apply the ideas and techniques of derivatives to solve compound
interest, continuous interest, effective interest rate, and present
value business models.
21. Calculate the Riemann sum for a given function, partition and
collection of evaluation points.
22. Describe a definite integral as the limit of a Riemann sum.
23. Determine anti-derivatives of basic algebraic functions.
24. Calculate values of definite integrals using anti-derivatives and
areas.
25. Apply substitution techniques to integrate basic functions.
26. Apply the ideas of definite integrals to solve problems of areas.
27. Calculate the average value of business models using the definite
integral.
28. Apply the ideas and techniques of the definite integral to
evaluate consumer/producer surplus, future/present value of
income streams, and annuity business models.
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