CATALOG DESCRIPTION: MATH 141 (GQ) Calculus with
Analytic Geometry II (4) 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.
PREREQUISITE: Math 140 or a score of 4 or 5 on AP Calculus AB Exam.
TEXT: Calculus (Single Variable) , Sixth Edition, (OR) Calculus, Sixth
Edition, by James Stewart, published by
Thomson (Brooks/Cole). An electronic version of the text (e-text) is available
chapter by chapter through
COURSE FORMAT: There are four 50-minute lectures each week. The sections
covered in lectures are listed at the
end of this syllabus.
MATH 141 LEARNING OBJECTIVES :
Upon successful completion of Math 141, the student should be able to:
1. Differentiate exponential, logarithmic, and inverse trigonometric functions.
2. Integrate exponential, logarithmic, and inverse trigonometric functions.
3. Recognize integrands for which integration by parts is appropriate.
4. Use the formula to integrate by parts.
5. Use techniques for integrals of products of sines and cosines.
6. Use techniques for integrals of secants and tangents.
7. Use techniques of trigonometric substitution to integrate various forms of
integrands.
8. Complete the square to express an irreducible quadratic polynomial as a sum
or difference of squares.
9. Perform polynomial long division to reduce an integrand to a more easily
integrated form.
10. Use the technique of partial fraction decomposition to reduce an integrand
to a more easily integrated form.
11. Given a random integration problem, choose the proper method and proceed
with integration.
12. Identify indeterminate limit forms.
13. Evaluate limits using L’Hospital’s Rule.
14. Recognize improper integrals and put in proper form for determination.
15. Determine if an improper integral diverges or converges (and if so, to
what?).
16. Identify and compare different types of sequences.
17. Determine if a sequence diverges or converges (and if so, to what?).
18. Recognize famous series in standard and non-standard form.
19. Apply infinite series tests for convergence and divergence.
20. Find the interval of convergence and radius of convergence for a given power
series.
21. Generate power series representations of some functions from a geometric
series perspective.
22. Generate power series representations of some functions from a Taylor Series
perspective.
23. Recognize and manipulate important Maclaurin Series (e^{x}, sin x, cos x,
tan^{-1}x, 1/(1-x)) by differentiation,
integration, and substitution.
24. Find the nth degree Taylor Polynomial of a function f at a point a and
determine the error associated with the
estimate.
25. Sketch graphs of curves defined parametrically.
26. Use calculus techniques to analyze the behavior of graphs of parametrically
defined curves.
27. Sketch graphs of polar equations.
28. Find slopes of tangents to polar-defined curves.
29. Find points of intersection of two or more polar functions.
30. Find areas enclosed by polar-defined curves.
CALCULATORS: A graphics calculator is useful as a study and learning tool
when used appropriately, but it is not
essential. Calculus is a collection of ideas that is not mastered through
calculator skills. No calculators are allowed on
quizzes, midterms, or on the final examination.
TUTORS AND MATH CENTER: Free mathematics tutoring is available at the
Math Center located in 220 Boucke
Building. For more information, go to the Math Center webpage. If you need extra
help, a (paid) tutors list maintained
by the Mathematics Department Undergraduate Office is available on-line at
EXAMINATIONS: Two 75-minute evening examinations will be given during the
semester and a comprehensive
final examination will be given during the final examination period. NO books,
notes, or calculators may be used on
the examinations. You must bring your University ID card to all exams. The
examinations will be given from 8:15 to
9:30 PM on the following dates:
Midterm Examination I | 8:15, Tuesday, February 17 |
Midterm Examination II | 8:15, Tuesday, March 31 |
Rooms for the examinations will be announced by your instructor at a later date
and may also be found on the bulletin
board outside 104 McAllister.
CONFLICT EXAMINATIONS: For the two mid-semester examinations, there is a
conflict examination from
6:50 PM to 8:05 PM on the same night as the regular examination.
Who may take the Conflict Exam? If you have a valid conflict with the regular
examination time, such as a class or
other scheduled activity, you may sign up for the conflict exam. Personal
business such as travel,
employment, weddings, graduations, or attendance at public events such as
concerts, sporting events,
etc. is not a valid excuse.
How and when to sign up for the Conflict Exam. Students must sign up for the
Conflict Exam in class, with your
instructor, on a pink form. The student is responsible for knowing the room and
time of the conflict
examination. This information is on top of the pink form. Your instructor must
turn in the pink form 2 class
days prior to the examination date. If you have not signed up with your
instructor, you will not be allowed to
take the conflict exam.
Instructions on Conflict Exam night. The student is responsible for knowing the
room and time of the conflict
examination. Students must bring their University ID to the conflict
examination. The ID will be
checked by the proctor. Although the conflict examination will end at 8:05 PM,
no student will be
permitted to leave the examination room before 8:10 PM. Any student who leaves
before 8:10 PM will
receive a grade of zero on the examination and will not be allowed to retake it.
MAKEUP EXAMINATIONS: A makeup exam will be given about a week following the
regularly scheduled exam.
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.
Students who do not have a
valid reason for missing the examination, such as forgetting the date, time, or
room of an examination, are
permitted to schedule the makeup, but 20 points will be deducted from their
score. Students who have taken
either the regularly scheduled examination or conflict examination are not
permitted to take the makeup
examination. Students who have not signed up for the makeup with their
instructor will not be allowed to take
the exam. The makeup examinations are given from 6:30 to 7:45 PM on the evenings
listed below:
Makeup Examination I | 6:30, Monday, February 23 |
Makeup Examination II | 6:30, Monday, April 6 |
How and when to sign up for the Makeup Exam. Students must sign up for the
Makeup Exam in class, with your
instructor, on a yellow form, as soon as possible following the regular exam
date. The student is
responsible for knowing the room and time of the makeup examination. This
information is on top of the
yellow form. Your instructor must turn in the yellow form 2 class days prior to
the examination date. If you
have not signed up with your instructor, you will not be allowed to take the
makeup exam.
Instructions on Makeup Exam night. Students are responsible for knowing the room
and time. On the day of the
exam the room will be posted on the door of 104 McAllister. Students must bring
their University 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 instructor with the approval of the course coordinator and must be
completed no later than one
week after the scheduled makeup examination.
FINAL EXAMINATION: The final examination will be given during the week, May 4-8,
2009. The final
examination may be scheduled on any day during the final examination period. Do
not plan to leave University
Park until after Friday, May 8, 2009. Students may access their final exam
schedule Monday, February 16, through
their e-lion account. 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 e-lion between February 16 and March 8. Conflict final examinations
cannot be scheduled
through mathematics department, and there will be no sign up sheet in 104
McAllister for the final conflict
examination. Students who miss both the regular and conflict final examinations
due to a valid and documented
reason, such as illness, may be allowed to take a makeup final examination. If
the student does not have a valid reason,
at least a 30-point penalty will be imposed. 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.
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. A baccalaureate student is
limited to 16 late drop credits. The late
drop deadline for Spring 2009 is April 10, 2009.
GRADES: Your course grade will be determined by your exam scores and a
homework/quiz score (labeled “QZ” by
Testing Services).
Total possible points follow:
Examination I | 100 |
Examination II | 100 |
Homework and/or quizzes | 100 |
Final Examination | 150 |
Total | 450 |
The exact point requirements for each letter grade will be decided at the end of
the course.
A typical distribution follows:
Guaranteed grade-line cutoffs updated 4/4/09
Grade | %-score | Points | New % | New Points |
A, A- | 90-100 | 405-450 | 89-100 | 400-450 |
B+, B, B- | 80-89 | 360-404 | 79-88 | 355-399 |
C+, C | 70-79 | 315-359 | 69-78 | 310-354 |
D | 60-69 | 270-314 | 59-68 | 265-309 |
F | 0-59 | 0-269 | 0-58 | 0-264 |
After the second exam and before the late-drop deadline the guaranteed
grade-line cutoffs for the major grades (A, B,
C, D, F) will be provided to facilitate your planning for the rest 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 the higher
grade. For the reason 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, homework
and/or quizzes and final
examination. There is no "extra-credit" work.
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.
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.
Academic dishonesty includes, but is no limited to, cheating, plagiarizing, […],
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
academic work of other students. […] A student charged with academic dishonesty
will be given
oral or written notice of the charge by the instructor. If students believe that
they have been falsely
accused, they should seek redress through informal discussions with the
instructor, the department
head, dean or campus executive officer. If the instructor believes that the
infraction is sufficiently
serious to warrant the referral of the case to Judicial Affairs, or if the
instructor will award a final
grade of F in the course because of the infraction, the student and instructor
will be afforded formal
due process procedures.
From Policies and Rules, Student Guide to the University Policy 49-20.
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.
QUESTIONS, PROBLEMS, 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 address is given
below.
SUGGESTED LECTURE-BY-LECTURE BREAKDOWN
WEEK | DAY | DATE | SECTION(S) | TOPIC | COMMENTS |
1 | Monday | Jan 12 | Introduction | Intro | CLASS BEGINS |
Tuesday | Jan 13 | 7.1 | Inverse Functions | ||
Wednesday | Jan 14 | 7.1 | Inverse Functions | ||
Thursday | Jan 15 | ||||
Friday | Jan 16 | 7.2^{*} | The Natural Logarithmic Function | Pages 421-429 | |
2 | Monday | Jan 19 | No Class | MARTIN LUTHER KING DAY | |
Tuesday | Jan 20 | 7.2^{*} | The Natural Logarithmic Function | Pages 421-429 | |
Wednesday | Jan 21 | 7.3^{*} | The Natural Exponential Function | DROP/ADD ENDS | |
Thursday | Jan 22 | ||||
Friday | Jan 23 | 7.3^{*} | The Natural Exponential Function | Pages 430-437 | |
3 | Monday | Jan 26 | 7.4^{*} | General Log and Exp Functions | Pages 438-446 |
Tuesday | Jan 27 | 7.4^{*} | General Log and Exp Functions | ||
Wednesday | Jan 28 | 7.6 | Inverse Trigonometric Functions | Pages 438-446 | |
Thursday | Jan 29 | ||||
Friday | Jan 30 | 7.6 | Inverse Trigonometric Functions | ||
4 | Monday | Feb 2 | 8.1 | Integration by Parts | |
Tuesday | Feb 3 | 8.1 | Integration by Parts | ||
Wednesday | Feb 4 | 8.2 | Trigonometric Integrals | ||
Thursday | Feb 5 | ||||
Friday | Feb 6 | 8.2 | Trigonometric Integrals | ||
5 | Monday | Feb 9 | 8.3 | Trigonometric Substitution | |
Tuesday | Feb 10 | 8.3 | Trigonometric Substitution | ||
Wednesday | Feb 11 | 8.4 | Integration of Rational Functions/Partial Fractions | ||
Thursday | Feb 12 | ||||
Friday | Feb 13 | 8.4 | Partial Fractions | ||
6 | Monday | Feb 16 | 8.5 | Strategies for Integration | |
Tuesday | Feb 17 | Review | Review | EXAM 1 | |
Wednesday | Feb 18 | 7.8 | Indeterminate Forms/L’Hospital’s Rule | ||
Thursday | Feb 19 | ||||
Friday | Feb 20 | 7.8 | Indeterminate Forms/L’Hospital’s Rule | ||
7 | Monday | Feb 23 | Rates of Growth | Relative Rates of Growth | Not in Text |
Tuesday | Feb 24 | Rates of Growth | Relative Rates of Growth | Not in Text | |
Wednesday | Feb 25 | 8.8 | Improper Integrals | ||
Thursday | Feb 26 | ||||
Friday | Feb 27 | 8.8 | Improper Integrals | ||
8 | Monday | Mar 2 | 12.1 | Sequences | |
Tuesday | Mar 3 | 12.1 | Sequences | ||
Wednesday | Mar 4 | 12.2 | Series | ||
Thursday | Mar 5 | ||||
Friday | Mar 6 | 12.2 | Series | ||
9 | Monday | Mar 9 | SPRING BREAK | ||
Tuesday | Mar 10 | SPRING BREAK | |||
Wednesday | Mar 11 | SPRING BREAK | |||
Thursday | Mar 12 | SPRING BREAK | |||
Friday | Mar 13 | SPRING BREAK | |||
10 | Monday | Mar 16 | 12.3 | Integral Test | |
Tuesday | Mar 17 | 12.3 | Integral Test, p-series | ||
Wednesday | Mar 18 | 12.4 | Comparison Tests | ||
Thursday | Mar 19 | ||||
Friday | Mar 20 | 12.4 | Comparison Tests | ||
11 | Monday | Mar 23 | Alternating Series | ||
Tuesday | Mar 24 | Alternating Series, Error Estimation | |||
Wednesday | Mar 25 | Absolute Convergence; Ratio & Root Tests | |||
Thursday | Mar 26 | ||||
Friday | Mar 27 | Absolute Convergence; Ratio & Root Tests | |||
12 | Monday | Mar 30 | 12.7 | Strategies for Testing Series | |
Tuesday | Mar 31 | Review | Review (don’t forget 7.8 & 8.8) | EXAM 2 | |
Wednesday | Apr 1 | 12.8 | Power Series | ||
Thursday | Apr 2 | ||||
Friday | Apr 3 | 12.8 | Power Series | ||
13 | Monday | Apr 6 | 12.9 | Reps of Functions as Power Series | |
Tuesday | Apr 7 | 12.9 | Reps of Functions as Power Series | ||
Wednesday | Apr 8 | 12.10 | Taylor & Maclaurin Series | ||
Thursday | Apr 9 | ||||
Friday | Apr 10 | 12.10 | Taylor & Maclaurin Series | LATE DROP DEADLINE | |
14 | Monday | Apr 13 | 12.11 | Apps of Taylor Polynomials | |
Tuesday | Apr 14 | 12.11 | Apps of Taylor Polynomials, Error Approx | ||
Wednesday | Apr 15 | 11.1 | Curves Defined by Parametric Equations | ||
Thursday | Apr 16 | ||||
Friday | Apr 17 | 11.2 | Calculus with Parametric Curves | ||
15 | Monday | Apr 20 | 11.2 | Calculus with Parametric Curves | |
Tuesday | Apr 21 | 11.3 | Polar Coordinates | ||
Wednesday | Apr 22 | 11.3 | Polar Coordinates | ||
Thursday | Apr 23 | ||||
Friday | Apr 24 | 11.4 | Areas in Polar Coordinates | ||
16 | Monday | Apr 27 | 11.4 | Areas in Polar Coordinates | |
Tuesday | Apr 28 | Review Ch 11 | Parametric, Polar | ||
Wednesday | Apr 29 | Review Ch 12 | Series | ||
Thursday | Apr 30 | ||||
Friday | May 1 | Review, Ch. 7-8 | Integrals, L’Hospital | CLASS ENDS |