Calculus (math-shu 131) PDF

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Calculus – MATH-SHU 131 1 Course description This course presents the foundations of calculus for functions of a single variable. Topics addressed include limits, continuity, rules of differentiation, approximation, antiderivatives, indefinite and definite integrals, the fundamental theorem of calculus, integration techniques, and improper integrals. [Prerequisite: Placement Examination or a grade of C or better in MATH-SHU 9.]

1.1 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; horizontal and vertical asymptotes; linear approximation; the mean value theorem; critical points and inflection points; indeterminate forms; graphing functions and their derivatives; optimization; the definite integral; the Fundamental Theorem of Calculus; integration by substitution; integration by parts; computing volumes and areas using an infinitesimal description; improper integrals.

1.2 The team Coordinator: Prof.2Roberto Fernández Lectures:

Profs.2Eric Endo, Roberto Fernández

Recitation:

Drs. Vlad Margarint, Tong Xuan Nguyen, Zhuang Su

1.3 Contact Communications regarding special situations should be sent to the Calculus Instructor, Professor Endo, at the address [email protected]. This includes notification of absences, time conflicts and general requests or complaints.

1.4 Textbook The textbook is “James Stewart/Daniel Transcendentals, Metric Version, 9th edition.”

K.

Clegg/Saleem

Watson.

Calculus:

1.5 Program The tentative plan for the 28 lectures is as follows: Topic Overview Limits: definition techniques Infinite Limits. Formal definition Continuity Limits at infinity

Section – and 2.2, 2.3

Tangent line and derivative

Topic Graph sketching The area problem

Section 4.5 5.1

2.3, 2.4

Definite integral

5.2

2.5 2.6

Exam 2 Antiderivatives. The Fundamental Theorem of Calculus Indefinite Integrals. Substitution Area and volume Integration by parts Integration of rational functions

–

2.7, 2.8

Differentiation rules 3.1 Product and quotient rules 3.2, 3.3 Chain rule and inverse 3.4 functions

4.9, 5.3

5.4, 5.5 6.1, 6.2 7.1 7.4

Early

Exam 1 – Implicit and log 3.5, 3.6 differentiation Linearization 3.10 Extreme values and mean 4.1, 4.2 value Monotonicity and concavity 4.3 Indeterminate forms 4.4 Optimization 4.7

Improper integrals Length of a curve

7.8 8.1

Area of surfaces of revolution 8.2 Review – Review Final Exam

– –

For some sections, supplementary text will be provided through NYU-Brightspace.

1.6 Weekly schedule The course consists of two lectures and one recitation session every week, for 14 weeks. Each class lasts 75 minutes, amounting to 52.5 hours in class. Each student is enrolled in one lecture section and one recitation section. You can see your section numbers, schedule and classroom on albert.nyu.edu. In addition to the classes, there is a weekly lab with a number of activities. The lab is designed for students who have failed a quiz or an exam but other students are also welcome. During the first two weeks there are many adjustments. To avoid missing a quiz, students must recheck Albert on Sep 02 and Sep 09 for changes in the schedule.

1.7 Weekly lab The Calculus Lab takes place each Wednesday 19:15-20:30 except Sep 01. The lab offers to students additional time for supervised work in which to review the material and address particular difficulties with it. Also, during some lab sessions students will be able to catch up on some failed quizzes and to take practice exams. The lab is open to every Calculus student, and attendance becomes a requirement for students failing to get C or higher on a quiz or an exam. In particular, performance in the Lab for these students will be a factor in deciding on borderline grades.

1.8 Office hours Office hours will be published and updated on NYU-Brightspace. If the schedule conflicts with other classes or student work shifts, students should contact the Calculus instructor (Professor Endo), who will be happy to accommodate a different time. Please recheck office hours every Sunday as there may be changes.

1.9 Subject to Change Statement The syllabus and course schedule may be subject to change. Changes will be communicated via email and in NYU LMS (Brightspace). It is your responsibility to check email messages and course announcements to stay current in the online phase of the course.

2 Participation and classroom norms 2.1 Mandatory lecture attendance Students are expected to attend and actively participate in every class. We will organize a Zoom session for each lecture to teach to in-person students (using the projectors and the screens in the classroom) and to synchronous (remote) students. To avoid confusion, a remote student classifies as one that is not able to attend the class in person but only virtually temporarily or for the entirety of the Fall Term. At the moment, included to this classification are students who travelled in medium or high-risks areas in Chinese Mainland during the Summer break and are now subject to health monitoring measures (such as quarantine), or

students who will not be able to return back to Shanghai indefinitely due to international travel restrictions. We created recurring Zoom meetings through NYU-Brightspace.

2.2 Mandatory recitation attendance Students are expected to attend and actively participate in every recitation. Vlad Margarint and Zhuang Su are assigned to teach for in-person students, and Tong Xuan Nguyen is assigned to teach for remote students.

2.3 Punctuality Students must arrive before class starts and leave after it is dismissed. Students who arrive late or leave early cause unnecessary perturbations to the course development. Repeated tardiness or early departures will be noted and result in the final course grade being rounded down.

2.4 Electronic devices During the lectures, the instructor will ask the students to scan QR codes to interact with the material. However, all electronic devices must be in silent mode during each class meeting. This includes phones, cameras, tablets and laptops. During the recitations and Labs, 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.

3 Grading of Assignments 3.1 Grade breakdown The evaluation is based on weekly quizzes and four exams with the following weight, date and focus: Paper

Weight

Participati on

5%

Homework

10%

see below

Contents of previous week

Quizzes

10%

see below

Exercise list of previous week

Exam 1

20%

Exam 2 Final Exam

25% 30%

Tentative date

Tentative topics

–

September 29 November 3 Finals week

–

Limits, continuity, definition of derivatives. Differentiation, study of functions Integration, applications and overview

The homework and the quizzes are the average of the grade for all semester.

3.2 Course Policies  Exams and quizzes will be closed book and closed note, and without calculators.  Quizzes will be given at the beginning of every recitation session, both in-person and remote.  The grade of the Quizzes will be showed in the Gradescope. Check the NYU-Brightspace to find the Entry Code.  Exams will be held during Calculus Lab.  The Final Exam will contain bonus questions for Midterm 1 and bonus questions for Midterm 2 that are worth 15 points each. Each Midterm grade with the additional score

of the bonus questions cannot exceed 100 points. If it exceeds, the grade is 100.  No grades will be dropped.  A student who fails to get C or higher on a quiz is required to attend the subsequent lab session. Likewise, a student who fails to get C or higher on an exam is required to attend all the subsequent lab sessions until the next exam. It is the student’s responsibility to check the gradebook and determine if attendance to the Lab is required.  A computer grading program called WebAssign will be used for homework problems assigned from the text (see the next paragraph for log-in information). The WebAssign program also includes access to an electronic version of the textbook. Homework will be due at 11:59pm on the due date. Late homework will receive 0 points.  Instructions for WebAssign: To create an account for our class, go to http://webassign.net and click on the “Enter Class Key” button on the upper right hand side. The class key will be announced through Brightspace.You must do this even if you have used WebAssign in the past or are using it for another course this semester. You will only need to enter this class key once.

3.3 Excused absences on quizzes and exams If a student has to miss a class or exam, their absence may be excused at the sole discretion of the Calculus Coordinator. The student must notify the instructor at [email protected] as soon as they aware of the restraint, and definitely before the class or exam takes place. Absences not communicated beforehand will not be excused under any circumstances. If an absence is excused and corresponds to a quiz or exam, the coordinator shall decide on whether a make-up is necessary or other exams will suffice for performance assessment. Absences due to religious observances It is NYU policy to allow members of any religious group to absent themselves from classes when compliance with their religious obligations requires it. Students who wish to excuse an absence for religious reasons are expected to notify the Calculus Coordinator beforehand as soon as they are aware of the restraint.

3.4 Paper retention, gradebook and grade review requests Once a quiz or exam is graded, it will be uploaded on Gradescope. From that day, students have from Monday, after the quiz or exam is released, until Tuesday at 11:59 PM to request a grading review on the Gradescope. After Wednesday, requests will no longer be accepted. For the Lab quiz, students have from Thursday, after the quiz or exam is released, until Friday at 11:59 PM to request a grading review on the Gradescope. After Saturday, requests will no longer be accepted.

4 General policies on grading The cutoffs will be the following: Final grade

Course grade

94.00-99.99 A 90.00-93.99 A87.00-89.99 B+ 83.00-86.99 B 80.00-82.99 B75.00-79.99 C+ 70.00-74.99 C 60.00-69.99 C55.00-59.99 D+

50.00-54.99 D 00.00-49.99 F 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.

5 Public Health Requirements and COVID-19 Student Code of Conduct You are expected to comply with the COVID-19 Student Code of Conduct. If you violate the COVID-19 Student Code of Conduct or fail to follow your instructor's related warnings, you may be asked to leave the classroom and/or may be subject to disciplinary action. You may review the Code on NYU Shanghai’s Community Standards page.

6 Academic integrity Academic integrity is the pursuit of scholarly activity in an open, honest and responsible manner. It is a basic guiding principle for all academic activity at NYU-Shanghai, and all members of the University community are expected to act in accordance with this principle. NYU has an established academic integrity policy, described at the web address: https://www.nyu.edu/about/policies-guidelines-compliance/policies-and-guidelines/academic-integrity-for-students-at-nyu.html

Students who receive help on any exam or quiz via books, notes, classmates, watches, cell phones, calculators, etc., will receive grade F in the course. Depending on the severity of the violation, the university administration may impose further penalties such as suspension or expulsion.

7 Academic Honesty/Plagiarism Carefully read NYU Shanghai’s Statement on Academic Integrity (in the Undergraduate Bulletin). Breaches of academic integrity could result in failure of an assignment, failure of the course, or other sanctions, as determined by the Academic Affairs office.

8 Resources and support 8.1 Disability Disclosure Statement NYU is committed to providing equal educational opportunity and participation for students with disabilities. It is NYU Shanghai’s policy that no student with a qualified disability be excluded from participating in any NYU Shanghai program or activity, denied the benefits of any NYU Shanghai program or activity, or otherwise subjected to discrimination with regard to any NYU Shanghai program or activity. Any student who needs a reasonable accommodation based on a qualified disability is required to register with the CSD for assistance. Students can

register online through the Moses Center and can contact the Director of the Academic Resource Center with questions or for assistance.

8.2 Title IX Compliance Title IX of the Education Amendments of 1972 (Title IX) prohibits discrimination on the basis of sex in educational programs. It protects victims of sexual or gender-based bullying and harassment and survivors of gender-based violence. Protection from the discrimination on the basis of sex includes protection from being retaliated against for filing a complaint of discrimination or harassment. NYU is committed to complying with Title IX and enforcing University policies prohibiting discrimination on the basis of sex. Mary Signor, Executive Director of the Office of Equal Opportunity, serves as New York University’s Title IX Coordinator. The University’s Title IX Coordinator is a resource for any questions or concerns about sex discrimination, sexual harassment, sexual violence, or sexual misconduct and is available to discuss your rights and judicial options. University policies define prohibited conduct, provide informal and formal procedures for filing a complaint and a prompt and equitable resolution of complaints. For more information, see: https://www.nyu.edu/about/policies-guidelines-compliance/equal-opportunity/title9.html

Links ● ● ● ● ●

to the Title IX Policy and related documents: Sexual Misconduct, Relationship Violence, and Stalking Policy Procedures for Complaints Against Students Procedures for Complaints Against Employees Resource Guide for Students Resource Guide for Employees

9 Academic Resources ARC Services The Academic Resource Center (ARC) offers both individual, one-on-one tutoring as well as group sessions in a variety of ways, in a variety of courses. You can log on to WCOnline to book an appointment with a Global Writing & Speaking Fellow or a Learning Assistant (LA). The Global Writing & Speaking Fellows conduct individual consultations on writing, speaking, reading, and academic skills coaching. LAs provide both individual and small-group tutoring support in over 30 STEM, Business, Economics, IMA/IMB, and Chinese Language classes. Visit shanghai.nyu.edu/arc for more information about ARC services.

Library Support Library Services The Library is available to support your research needs. They have access to over 27,000 print resources, 2,000 DVDs, and 1,000 databases (including over a million e-books, as well as streaming audio and video and image databases). Librarians with expertise in your research topic are available to meet either in person or online by appointment or by email to help you navigate the research process. Our library team features experts in Business, Arts & Humanities, STEM, Social Sciences & Economics, and data tools & resources. Ask us how we can assist you in developing a research question and formulating a research strategy, to selecting databases, requesting materials, and citing your sources. Visit shanghai.nyu.edu/library for more information on: ● 24/7 access to e-books, e-journals, streaming media, and databases ● Booking one-on-one consultations for research help ● Asking the Library questions via chat or email

Electronic Reserves Students can access course readings using their NYU credentials for courses they currently

enrolled in at https://ares.library.nyu.edu/.

Interlibrary Loan Service For materials not available to you immediately, you can request scanned copies of a book chapter or journal article through our Interlibrary Loan (ILL) service. If you don't know which chapter you need, you can request a Table of Content through ILL....