Math 141
Calculus II
Fall 2022
Course Description: Math 141 (GQ) Calculus with Analytic Geometry II (4 credits) Derivatives, integrals, applications; sequences and series; analytic geometry; polar coordinates. Students
may take only one course for credit from MATH 141, 141B, 141E, 141G, and 141H.
Prerequisites: Math 140 or a score of 4 or 5 on AP Calculus AB Exam.
Required Materials:
1. Textbook: Calculus: Early Trancendentals by Jon Rogawski, Colin Adams, and Robert
Franzosat. 4th ed. 2019. MacMillan.
2. Online: An activated Achieve account.
Options for Purchasing the Required Materials: The required materials are available
in three different forms (you need to purchase only one):
• Electronic Package: isbn 9781319371883. This option provides access to the ebook version
of the course materials through a single Achieve account.
• Print Package: isbn 9781319371869 This option includes a hardback edition of the textbook
and access to the ebook. Note: The print option includes an activation code for the ebook
as well, so anyone who purchases the print option will also have access to the ebook version
through their Achieve account.
• Loose-Leaf Package: isbn 9781319371845. This option includes a printed loose-leaf edition
of the textbook and access to the ebook. Note: As with the Print option he loose-leaf option
includes an activation code for the ebook as well, so anyone who purchases the loose-leaf
option will also have access to the ebook version through their Achieve account.
Where to Purchase the Required Materials:
• Electronic: Directly through Achieve — this is simplest and following the link on
your Canvas page will allow you to purchase access.
• Print & Loose-Leaf:
(i) Directly through Achieve.
(ii) The Penn State University Bookstore.
Important Notes:
• Please do not purchase or rent any edition of the textbook through any source
not listed above. Currently, only the publisher and the University Bookstore offers the
edition of the textbook used in this class. Please check with your instructor before buying
or renting through another source.
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• If you have already purchased these materials for Math 140, there is no need to purchase
them again.
• Regardless of how you purchase access, you will need to click the link on your Canvas page
to enroll in your Achieve section.
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Learning Objectives: This course satisfies the General Education learning objectives Key
Literacies and Critical and Analytical Thinking. Upon successful completion of Math 141, the
student should be able to:
5.3/5.8
• Distinguish between an indefinite integral / specific antiderivative / definite integral and a
general solution / specific solution / value of a specific solution at a specified input.
• Calculate antiderivatives involving constant factors, sums/differences, xp , ex , sin x, cos x,
1
1
sec2 x, sec x tan x, bx , √1−x
2 , x2 +1 . (That is, the “basic antiderivative rules” that are obtained
simply by reversing Chapter 3 derivative formulas.)
• Use algebra to rewrite certain integrals into more basic forms that can be evaluated using
basic antiderivative rules.
• Calculate antiderivatives involving linear inside functions.
5.7
• Use substitution to evaluate integrals like
R
2
xex dx.
R 2
• Explain why substitution cannot evaluate integrals like ex dx.
R √
• Use substitution to evaluate integrals like x2 x + 1 dx. (That is, where using both u =
u(x) and x = x(u) is needed to convert the dx integral to a du integral.)
• Evaluate definite integrals of functions given incomplete data (e.g. table data), where changing bounds is necessary.
• Understand in terms of transformations the du → u0 (x) dx conversion and how the bounds
change when using substitution with linear inside functions.
9.1
• Classify differential equations by order (first, second, ...) or type (autonomous, non-autonomous).
• Check whether a function satisfies a differential equation.
• Given an ansatz, determine the value(s) of unknown constants in the ansatz that guarantee
it satisfies a differential equation / initial value problem.
• Use separation of variables to solve separable differential equations.
• Use separation of variables to answer quantitative questions about solutions of initial value
problems. E.g. how long does it take for there to be an effective level of medicine in a
patient’s bloodstream? When does the bank account reach zero balance?
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9.2
• Given a differential equation, identify the independent variable, the dependent variable, and
any parameter(s).
• Translate a verbal description of a fundamental law into a differential equation / initial value
problem.
• Use Newton’s Law of Cooling to develop models for temperature change.
• Understand various population growth models in the context of birth rates, death rates,
and/or carrying capacity.
• Formulate differential equations / initial value problems for the balance in a bank account
subject to compound interest and deposits/withdrawals.
• Formulate differential equations / initial value problems for IV medicine problems.
• Use sign analysis to classify the stability of equilibrium solutions of autonomous equations.
• Use stability analysis to determine qualitative behavior of solutions to initial value problems for various models introduced previously (terminal velocity, Newton’s Law of Cooling,
population models, IV medicine problems, banking problems). Qualitative behavior is increasing/decreasing behavior and/or long-term behavior.
7.1
• Use integration by parts to evaluate integrals of the form
R
R
R
xn eax dx, xn sin(ax) dx, xn cos(bx) dx.
R
R
R
• Use integration by parts to evaluate integrals of the form xp ln x dx, arctan(ax) dx, arcsin(ax) dx.
• Use integration by parts to evaluate integrals given incomplete data (e.g. table data).
7.2
• Evaluate integrals of the form
R
sinn x cosm x dx, where n and m are non-negative integers.
• Evaluate integrals of the form
even.
R
secn x tanm x dx, except for the case of both n odd and m
7.3
• Evaluate integrals involving
substitution u = u(x).
√
√
a2 − x2 or a2 + x2 that cannot be evaluated with standard
7.5
• Evaluate integrals of proper rational functions whose denominators have simple linear factors,
repeated linear factors, and/or simple irreducible quadratic factors.
• Use partial fractions to solve models of logistic population growth.
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2.5/4.5
→0 →∞
, →∞ , (→ ∞) · (→ 0),
• Identify indeterminate forms →0
(→ ∞) − (→ ∞), (→ 1)→∞ , (→ 0)→0 , (→ ∞)→0 .
• Given a type of indeterminate form, provide examples with different behavior in order to
explain indeterminacy with concrete examples.
• Use algebra when possible to evaluate indeterminate limits.
• Use L’Hospital’s rule when necessary to evaluate indeterminate limits.
7.7
• Write improper integrals as limits of proper integrals in order to evaluate them or determine
that they diverge.
10.7
• Instead of determining linear approximations, find quadratic or cubic approximations of
functions near a specified input value.
10.1
• Understand and apply the definition of sequence convergence/divergence.
• Use limit laws, algebra, L’Hospital’s rule, or relative growth grates to investigate the convergence/divergence of various sequences.
• Understand and apply the definition and properties of bounded sequences and/or monotonic
sequences.
10.2
• Manipulate summation notation for infinite series.
• Understand and apply the definition of infinite series convergence/divergence.
• Use the nth Term Divergence Test to investigate the divergence of various series.
• Find closed-form, explicit expressions for partial sums of geometric series.
• Determine the sum of infinite geometric series or show that they diverge.
• Use patterns to set up geometric series models of discrete versions of continuous models
introduced previously, e.g. taking pills every 8 hours instead of taking IV medication, or
making a deposit every set amount of time instead of modeling with continuous deposits for
bank problems.
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10.3
• Use the Integral Test to investigate the convergence/divergence of various series.
• Decide whether a comparison test is appropriate for analyzing the convergence/divergence
of various series, and if so whether the Direct Comparison Test or Limit Comparison Test
is more appropriate.
10.4
• Use the Alternating Series Test to investigate the convergence of alternating series.
• Determine whether various series converge absolutely, converge conditionally, or diverge.
• Use the Alternating Series Error Bound to determine the maximum possible error in estimating the sum of a convergent alternating series with its nth partial sum.
10.5
• Use the Ratio and Root Tests to investigate the convergence/divergence of various series.
• Determine the best test to use to investigate the convergence/divergence of a given series.
10.6
• Determine whether or not a given series is a power series.
• Determine the radius and interval of convergence of a given power series.
• Use properties of power series to answer questions regarding power series convergence/divergence
with partial information.
• Use the geometric sum power series along with substitution, differentiation, or integration
to quickly find power series representations of given functions.
10.7
• Given a function f (x), determine its nth degree Taylor Polynomial centered at a given input
a.
• Determine the maximum possible error involved in estimating a function with its linearization.
• Determine the maximum possible error involved in estimating a function with its nth degree
Taylor Polynomial.
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10.8
• Given a function, determine information about its Taylor Series centered at a given input a;
or given a function’s Taylor series, determine information about the function.
• Use the table of “known” Maclaurin series to quickly find either the first few nonzero terms
of a series expansion of a given function, or find the full series using summation notation.
• Solve certain linear differential equations using power series that we could not solve due
to antiderivative formulas not being available. E.g. simple exponential growth with time
dependent harvesting/birthing.
• Perform basic complex arithmetic (sum / difference / multiplication / division / modulus /
conjugation).
• Use the xy-plane to visually represent complex numbers.
• Use Maclaurin series to understand Euler’s formula.
11.3
• Describe points in the xy-plane using polar coordinates.
• Write complex numbers in polar form.
• Provide polar inequalities to describe regions in the xy-plane.
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A Few Important Class Resources:
• Instructor Office Hours: To be announced during the first week of class.
• Tutoring: Free mathematics tutoring is available from Penn State Learning. Visit their
website (pennstatelearning.psu.edu/tutoring/mathematics) for details.
• Guided Study Group Leader: Penn State Learning employs a tutor to help with the Math
141 subject material exclusively. The tutor, called a Guided Study Group (GSG) leader will
be available every week at regular times. The GSG Leader for the Fall 2022 Semester is
To Be Announced
• Tutoring Hours: To be Announced
• Zoom room: To be Announced.
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Examinations: Three 75-minute evening examinations will be given during the semester and a
comprehensive final examination will be given during the final examination period. Absolutely no
books, notes, or calculators may be used during the examinations. You must bring your University
ID card to all exams.
Midterm I
Midterm II
Midterm III
Wednesday, September 21
Thursday, October 20
Monday, November 14
6:15-7:30 pm
6:15-7:30 pm
6:15-7:30 pm
Rooms for examinations will be announced by your instructor at a later date and may also be
found on the courses website when they are available. It is not permissible to take the exam in a
different instructor’s assigned room.
Conflict & Makeup Exam Policies In addition to the three regularly scheduled midterm
examinations, the math department provides two options for students who are unable to attend at
the scheduled time: a conflict exam and a makeup exam. Please be sure you know the difference.
• A conflict exam for each of the midterms is offered on the same night as the regularly
scheduled exam at a different time (your professor will announce the specific time). Students
who attend the conflict exam will not be permitted to leave the exam room before the end
of the time period.
• A makeup exam is scheduled on an evening different from that of the regularly scheduled
exam.
In order to qualify for either the conflict or makeup exam, you must have a valid conflict or makeup
reason. If you think you will not be able to take the regularly scheduled exam, and would like to
take either the conflict or makeup exam, you must
1. Contact your instructor to determine if you are eligible to take a conflict or makeup
makeup exam
2. Provide all necessary documentation where relevant or necessary,
3. Receive confirmation from your instructor that your are eligible for a conflict or
makeup exam, and
4. Sign up for the conflict or makeup exam using the online signup form (linked below) no
later than the specified deadline.
The online signup forms for both the conflict exam and the makeup exam are available here:
https://science.psu.edu/math/undergraduate/courses/course-information. It is the student’s responsibility to sign up before the deadline and to note the time and location of the makeup
or conflict exam.
Note: Students who miss an exam – including conflict or makeup exams – without a
valid reason and the approval of their instructor will receive a zero.
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Who May Take The Conflict Exam? If you have a valid conflict with the regular examination time, such as a class or another official university activity, you may sign up for the conflict
exam. If a student has not signed up for the conflict exam, he or she will not be permitted to take
the exam.
Instructions on Conflict Exam Night. The student is responsible for knowing the room
and time of the conflict examination. Each student must bring his or her University ID to the
conflict examination. The ID will be checked by the proctor. Although the conflict examination
will end at 6:05pm, no student will be permitted to leave the examination room before 6:10pm.
Any student who leaves before 6:10pm will receive a grade of zero on the examination and will
not be allowed to retake it.
Who May Take the Makeup Exam? Students who have a valid documented reason, such as
a class conflict or illness, during both the conflict and regular examination times are permitted
to schedule a makeup examination with no penalty. You must be prepared to verify the reason
for taking the makeup. Personal business, such as travel, employment, weddings, graduations, or
attendance at public events such as concerts, sporting events, and Greek Rush events, is not a valid
excuse. Forgetting the date, time or room of an examination is not a valid excuse. Students who
have taken either the regularly scheduled examination or conflict examination are not permitted
to take the makeup examination. The makeup examinations are given on the evenings and times
listed below:
Makeup Exam I
Makeup Exam II
Makeup Exam III
Tuesday, September 27
Wednesday, October 26
Thursday, November 17
6:15-7:30 pm
6:15-7:30 pm
6:15-7:30 pm
How and When to Sign up for the Makeup Exam: A students who is ill on exam night
must contact his or her instructor within 24 hours of the exam. Students must sign up for the
Makeup Exam at the provided signup link, as soon as possible following the regular exam date. The
online signup forms for both the conflict exam and the makeup exam are available here: https://
science.psu.edu/math/undergraduate/courses/course-information The student is responsible for knowing the room and time of the makeup examination. If a student has not signed up
with his or her instructor, the student will not be allowed to take the makeup exam.
Instructions on Makeup Exam Night: The student is responsible for knowing the room
and time of the makeup examination. Each student must bring his or her PSU ID to the makeup
examination. The ID will be checked by the proctor.
What If A Student Misses Both The Regularly Scheduled Exam and The Makeup
Exam? If a student misses both the regularly scheduled examination and the scheduled makeup
due to a valid, verifiable reason, it may be possible to take a makeup examination by appointment. All such makeup examinations must be scheduled through the classroom instructor with
the approval of the course coordinator and must be completed no later than one week after the
scheduled makeup examination. Personal matters such as travel, employment, weddings, graduations, or attendance at public events such as concerts, sporting events, and Greek Rush events,
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are not valid reasons. Forgetting the date, or time of examination is not a valid reason.
What if A Student Misses More Than One Week of Class at a Time? Students
who are unable to attend class or complete graded assignments for more than one week at a time
will be required to present documentation to verify their significant, prolonged illness. From UHS
Policies & Patient Resources:
“For routine illness-related absences, students should correspond directly with the faculty as soon
as possible regarding their situation, ideally, before they miss a class, exam, or other evaluative
activity.
University Health Services may provide verification of illness forms for significant prolonged illnesses or injuries lasting at least a week resulting in absence from classes.
When appropriate, students may request the verification during their clinician visit or send a secure message to their clinician or the Advice Nurse through myUHS at https://studentaffairs.
psu.edu/health/myuhs. If a student wants a verification of illness from University Health Services and has received care from an outside provider for a significant, prolonged illness, he/she
must provide appropriate documentation to the University Health Services director, 502A Student
Health Center, 814-865-6555.”
Barring emergencies, only one makeup opportunity is granted for each quiz or exam.
Websites, Calculators & Apps: A calculator, online problem solver, downloadable app, etc.
is an excellent tool for crunching numbers – especially when working real-world examples with
messy constants – as well as a useful study resource. If you do not have a scientific calculator,
websites such as Symbolab and Wolfram Alpha are an excellent resource for computations. Note,
however, that these tools are not needed to understand and apply the concepts of the course to
examples with simple coefficients (all arithmetic will be simple enough to do by hand.) No form
of calculators or electronic problem solver will be permitted on any of the homeworks,
quizzes, assignments, assessments, or exams for this course unless otherwise specified
by your instructor. Their use is a violation of Penn State’s Academic Integrity Policy.
Final Examination: The final examination will be given during the week, December 12-16,
2022. The final examination may be scheduled on any day during the final examination period. Do not plan to leave University Park until after Friday, December 16,
2022. Students may access their final exam schedules Monday, September 26, 2022 , through their
Lionpath accounts. Notification of conflicts is given on the student’s final exam schedule. There
are two types of conflict examinations: direct and overload. Direct conflicts are two examinations
scheduled at the same time. Overload examinations are three or more examinations scheduled
within a fifteen hour period, from the beginning of the first examination to the beginning of the
third examination. Students may elect to take the three or more examinations on the same day if
they wish or request a conflict final examination. A student must take action to request a conflict
exam through Lionpath between September 26 and October 16, 2022. Conflict final examinations
cannot be scheduled through the Mathematics department, and there will be no sign up sheet in
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class for the final conflict examination. Students who miss or cannot take the final examination
due to a valid and documented reason, such as illness, may be allowed to take a makeup final
examination at the beginning of the next semester. Personal business, such as travel, employment, weddings, graduations, or attendance at public events such, as concerts
and sporting events are not valid excuses. Forgetting the date, time, or room of an
examination is not a valid excuse. All such makeup examinations must be arranged through
the instructor with the approval of the course coordinator, and students in such a situation should
contact their instructor within 24 hours of the scheduled final examination. Students who have
taken the original final examination are not permitted to take a makeup examination.
Course Grades: Grades will be calculated from a total of 600 points, distributed as follows:
Midterm I
Midterm II
Midterm III
Homework & Quizzes
Final Exam
Total
100
100
100
150
150
600
points
points
points
points
points
points
Final course grades will be assigned as follows:
Grade
A
A−
B+
B
B−
C+
C
D
F
Raw Score
555-600 points
537-554 points
519-536 points
495-518 points
477-494 points
459-476 points
417-458 points
357-416 points
0 - 356 points
Percent Score
93% - 100%
90% - 92%
87% - 89%
83% - 86%
80% - 82%
77% - 79%
70% - 76%
60% - 69%
0% - 59%
Additional Notes:
1. Final Grade: Your final grade will be based exclusively on the midterm examinations,
section score, and the final examination. There is no extra-credit work.
2. Homeworks: There are two distinct types of homework assignments required for this
course.
(a) Written: This is the usual type of homework assignment. Your instructor will assign
problem sets to be submitted by a specified due date. Credit is given for writing full
and complete solutions to the problems assigned. A scanned copy of the completed
work must be submitted to your instructor through your Canvas account.
(b) Online homework. These assignments are completed online through your Achieve account. You are responsible for activating your Achieve account and verifying
access to the textbook online no later than class on Wednesday, August 24.
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3. Section Score: Your section score is assigned by your instructor and is calculated from
your homework and quiz scores as follows
• Online Homework: 25 points.
• Written Homework: 50 points.
• Quizzes: 75 points.
Deferred Grade: Students who are currently passing a course but are unable to complete the
course because of illness or emergency may be granted a deferred grade which will allow the student to have up to ten weeks from the final grade reporting deadline to complete the course. 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. Approval needs to be granted prior to the beginning
of the final exam period of the semester in which the course is taken. For more information see
https://www.registrar.psu.edu/grades/deferred.cfm.
Late-Drop: Students may add/drop a course without academic penalty within the first ten calendar days of the semester. A student may late drop a course within the first twelve weeks of the
semester but accrues late drop credits equal to the number of credits in the dropped course. The
late drop deadline for Fall 2022 is Friday, November 11, 2022.
Academic Integrity: All Penn State policies regarding ethics and honorable behavior apply
to this course (see links below for policy statements). Academic integrity is the pursuit of scholarly activity free from fraud and deception and is an educational objective of this institution.
All University policies regarding academic integrity apply to this course. Academic dishonesty
includes, but is not limited to, cheating, plagiarizing, fabricating of information or citations, facilitating acts of academic dishonesty by others, having unauthorized possession of examinations,
submitting work of another person or work previously used without informing the instructor, or
tampering with the academic work of other students. For any material or ideas obtained from
other sources, such as the text or things you see on the web, in the library, etc., a source reference
must be given. Direct quotes from any source must be identified as such. All exam answers must
be your own, and you must not provide any assistance to other students during exams. Any
instances of academic dishonesty WILL be pursued under the University and Eberly College of
Science regulations concerning academic integrity.
Academic dishonesty is not limited to simply cheating on an exam or assignment. The following is
quoted directly from the “PSU Faculty Senate Policies for Students” regarding academic integrity
and academic dishonesty:
Academic integrity is the pursuit of scholarly activity free from fraud and deception
and is an educational objective of this institution. Academic dishonesty includes,
but is not limited to, cheating, plagiarizing, fabricating of information or citations,
facilitating acts of academic dishonesty by others, having unauthorized possession
of examinations, submitting work of another person or work previously used without
informing the instructor, or tampering with the academic work of other students.
In an examination setting, unless the instructor gives explicit prior instructions to the contrary,
violations of academic integrity shall consist of any attempt to receive assistance from written or
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printed aids, from any person or papers or electronic devices, or of any attempt to give assistance,
whether the student doing so has completed his or her own work or not. Other violations include,
but are not limited to, any attempt to gain an unfair advantage in regard to an examination, such
as tampering with a graded exam or claiming another’s work to be one’s own. Failure to comply
will lead to sanctions against the student in accordance with the Policy on Academic Dishonesty
in the Eberly College of Science.
Students with Disabilities: Penn State welcomes students with disabilities into the University’s educational programs. Every Penn State campus has an office for students with disabilities.
Student Disability Resources (SDR) Web site provides contact information for every Penn State
campus: http://equity.psu.edu/sdr/disability-coordinator. For further information, please visit
Student Disability Resources Web site: http://equity.psu.edu/sdr.
Counseling and Psychological Services: Many students at Penn State face personal challenges or have psychological needs that may interfere with their academic progress, social development, or emotional wellbeing. The university offers a variety of confidential services to help
you through difficult times, including individual and group counseling, crisis intervention, consultations, online chats, and mental health screenings. These services are provided by staff who
welcome all students and embrace a philosophy respectful of clients’ cultural and religious backgrounds, and sensitive to differences in race, ability, gender identity and sexual orientation.
Counseling and Psychological Services at University Park (CAPS):
(http://studentaffairs.psu.edu/counseling/): 814-863-0395
Counseling and Psychological Services at Commonwealth Campuses:
(http://senate.psu.edu/faculty/counseling-services-at-commonwealth-campuses/)
Penn State Crisis Line (24 hours/7 days/week): 877-229-6400
Crisis Text Line (24 hours/7 days/week): Text LIONS to 741741
Educational Equity and Report Bias: Consistent with University Policy AD29, students
who believe they have experienced or observed a hate crime, an act of intolerance, discrimination,
or harassment that occurs at Penn State are urged to report these incidents as outlined on the
University’s Report Bias webpage: http://equity.psu.edu/reportbias/
Questions, Concerns, or Comments: If you have questions or concerns about the course,
please consult your instructor first. If further guidance is needed, you may contact the course
coordinator whose contact information is given below.
Course Coordinators:
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Joe Roberts, Associate Teaching Professor
104 McAllister Building
University Park, PA 16802
Telephone: 814-865-7528
Email: math141coord@psu.edu
David Nieves, Assistant Teaching Professor
408 McAllister Building
University Park, PA 16802
Email: math141coord@psu.edu
Please be sure to include your Name, Student ID, Course, and Section Number
in any correspondence.
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