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Calculus – MATH-SHU 121
Course description
This course presents the foundations of calculus by examining functions and their deriva- tives and integrals with a view towards applications. Topics addressed include basic techniques of differentiation and integration for functions of one variable, including lin- ear approximation, optimization, and modeling with differential equations, forming an essential treatment of calculus for any applied science.
Expected learning outcomes
At the end of this course, students will be able to define and apply concepts and tools such as: limits, derivatives and integrals of single-variable functions; linear approxima- tion; the mean value theorem; graphing functions and their derivatives; optimization; the fundamental theorem of Calculus; volume of solids and area of surfaces; integration by parts; improper integral.
Tentative calendar
Week Topics Textbook 1 Mathematical definition of limit. Basic rules. 2.2, 2.3, 2. 2 Evaluating limits. Continuity. 2.3, 2.4, 2. 3 Limits involving infinity. Derivative & tangent line. 2.6, 2.7, 2. 4 Differentiation rules. Product and quotient. 3.1, 3.2, 3. 5 Chain rule. Extreme values and Mean Value. 3.4, 4.1, 4. 6 Monotonicity & concavity. Antiderivatives. 4.3, 4. 7 The area problem. Definite integrals. 5.1, 5. 8 Fundamental Theorem of Calculus. Substitution. 5.3, 5.4, 5. 9 Area. Volume. Integration by parts. 6.1, 6.2, 7. 10 Length of a curve. Area of surfaces of revolution. 8.1, 8. 11 Indeterminate forms. Improper integrals. 4.4, 7. 12 Graph sketching. Optimization. 4.5, 4. 13 Implicit differentiation. Log differentiation. 3.5, 3. 14 Review
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Textbook
The textbook is “James Stewart. Calculus: Early Transcendentals, Metric Version ,” either 7th Edition (ISBN-9780538498876) or 8th Edition (ISBN-9781305272378).
An optional supplement is “ Complete Solutions Manual for Stewart’s Single Variable Calculus: Early Transcendentals , Cengage,” 7th Edition (ISBN-9780840049360) or 8th Edition (ISBN-9781305272620), on reserve at the library. Many Juniors and Sophomores have a copy of the 7th Edition they may be willing to sell, in which case they should provide the PDF version too. Exercise lists will be for the 7th Edition, and the correspondence with the 8th Edition will be indicated for the few exercises that have been reshuffled.
Weekly schedule
Each student is enrolled in one lecture section and one recitation section, as follows.
Section Days Time Room Instructor/Recitation leader 001 M&W 08:15-09:30 TBA Leonardo T. Rolla 002 M&W 11:30-12:45 TBA Vladas Sidoravicius 003 M&W 14:45-16:00 TBA Vladas Sidoravicius 004 Friday 09:45-11:00 TBA Robin Stephenson 005 Friday 11:30-12:45 TBA Robin Stephenson 006 Friday 14:45-16:00 TBA Robin Stephenson 007 Friday 09:45-11:00 TBA Mathieu Laurière 008 Friday 11:30-12:45 TBA Mathieu Laurière 009 Friday 14:45-16:00 TBA Mathieu Laurière 010 Friday 09:45-11:00 TBA Jérôme Casse 011 Friday 11:30-12:45 TBA Jérôme Casse 012 Friday 14:45-16:00 TBA Jérôme Casse
Online resources and announcements
The Calculus Team will share all the relevant material with students through a folder called “Calculus Fall 2017” on NYU-Drive. Log out of gmail and open drive.nyu.edu.
Announcements will be sent by e-mail through NYU-Groups. To review all past messages, log out of gmail and open groups.nyu.edu.
Office hours
Office hours will be published and updated on a file within the NYU-Drive folder. If the schedule conflicts with other classes or student work shifts, students should contact the Calculus Team, who will be happy to accommodate a different time.
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Exams and quizzes
Exams will be closed book and closed note, and calculators will not be allowed for exams. There will be four exams, on dates to be announced. Quizzes will be given either at the beginning of a recitation session or as homework. No grades will be dropped.
Excused absences
If a student has to miss a quiz or exam with a good justification, their absence may be excused at the sole discretion of the Calculus Team, or alternatively by the Aca- demic Affairs office. If the absence is excused, the corresponding grade will be replaced either by a make up of the quiz or exam, or by some average of the student’s other grades, at the sole discretion of the Calculus Team. An important requisite is to write to shanghai.calculus@nyu.edu as soon as the student is aware of the restraint, and definitely before the quiz or exam takes place.
Absences not communicated beforehand will not be excused under any circumstances.
No more than a total of two days of absence will be excused by the Calculus Team during the semester. Further absences will only be excused by the Academic Affairs office.
Accommodation of conflict exams
There are two types of conflicts. Direct conflicts are two examinations scheduled at the same time. Overload conflicts are three or more examinations scheduled on the same day.
In case of conflicting exams, it is the responsibility of the student to notify the instructor in a timely manner of their circumstances so that appropriate accommodations can be made. In this course, timely manner will be understood as two business days after the exam date is announced. If students do not inform the Calculus Team at shanghai.calculus@nyu.edu of conflicts within this lapse, the exam date will become definitive and accommodation requests will be denied. If conflicts arise after that, the student will have to try and accommodate with the instructors of the other courses involved in the conflict.
Paper retention
Quizzes and exams will be returned during the next recitation session once they are graded. After that, they will be kept for two more weeks and then disposed.
Self-assessment
Students in this class have very different backgrounds, needs and expectations. The university offers lectures, recitations, office hours, and peer tutors. It is for the students to find out which ones they should use and how. The three main variables for self-assessment
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and benchmarking are: (i) difficulty to follow the lectures, (ii) difficulty with the exercise lists, and (iii) performance on quizzes. Students who feel that they are starting to leg behind should contact their instructor and recitation leader immediately.
Participation and classroom norms
Attendance. Students will decide whether they should attend each class. There are no penalties for an unexcused absence besides missing the contents of that class.
Punctuality. Students are expected to arrive before class starts and leave after it is dismissed. Late students inevitably disturb the class and will not be allowed in.
Electronic devices. All electronic devices must be turned off prior to the start of each class meeting. This includes phones, cameras, tablets and laptops.
Recording the class. Photographing, filming or recording the instructor, classmates or the whiteboard is not allowed.
Grading
The tentative grade breakdown will be the following:
Item Weight Quizzes 10 Exam 1 15 Exam 2 20 Exam 3 25 Exam 4 30
The cutoffs for each course grade will only be decided at the end of the course. A total of 90% will probably suffice for A −, a total of 80% will probably suffice for B −, and a total of 70% will probably suffice for C. No lowest or highest grades will be dropped.
Each student’s course grade will depend solely on that student’s performance. There is no grade curving, grade normalization, or any form of extra credit.
A student who fails to observe classroom norms may have their course grade reduced.
During quizzes and exams, the possession of any electronic device, including cell phones, is not allowed, regardless of whether the student is actually using it or not. So is the use of books, notes, calculators, or any other object extraneous to the exam. A student who fails to observe these norms will receive grade zero on that test. Please note that this is part of the evaluation criterion adopted in this course. It is applied independently of eventual academic penalties carried out by the administration, for which the process is subject to university policies.
