MAT201Multivariable Calculus – Fall 2021
                                Course head     Andrew Yarmola (yarmola@math.princeton.edu)
                                  Instructors   János Kollár (kollar@math.princeton.edu)
                                                Jennifer Li (jenniferli@princeton.edu)
                                                Joaquín Moraga (jmoraga@math.princeton.edu)
                                                Samuel Pérez-Ayala (sp1248@princeton.edu)
                                                Ravi Shankar (rs1838@princeton.edu)
                                                John Sheridan (jts5@princeton.edu)
                                                Artane Siad (as4426@princeton.edu)
                                                Liyang Yang (liyangy@princeton.edu)
                                                Ruobing Zhang(ruobingz@math.princeton.edu)
                                    Lectures    Mondays&Wednesdays
                                    Precepts    Fridays
                                 Office hours    See Canvas Calendar
                                     Website    Canvas (https://canvas.princeton.edu)
                  Textbook and Material
                  Thomas’ Calculus: Multivariable, 14th edition by Joel R. Hass, Christopher E. Heil, Maurice
                  D. Weir, ISBN-13: 978-0134439020.
                  Wewill cover (most of) Chapter 12-16 of the text. Topics include: vector calculus, partial dif-
                  ferentiation and optimization, double and triple integrals in various coordinate systems, line and
                  surface integrals, as well as Green’s, Stokes’ and Divergence theorems.
                  Course structure
                  Lectures for the course will be on Mondays and Wednesdays. See the tentative schedule at
                  the end of the syllabus. Note, you are expected to read the relevant material from the textbook
                  as some of it may not be covered in lecture. Be aware that the course is fast-paced and it is
                  important to keep up with the reading and homework in order to do well. You are also expected
                  to participate in the weekly precepts where you will work with your peers and an instructor on
                  exercisesandconceptualproblems. Classparticipationanddiscussionarestronglyencouraged
                  andexpected. Pleaseaskquestionsifanythingisunclear,donothesitatetoattendofficehours,
                  contact you instructor if you need help, or use Ed Discussion to ask questions. Remember that
                  mathematics is learned mostly by thinking and working through problems. We are here to do
                  our best to help you find the correct tools and ideas to solve these problems, but it is your
                  participation that will make all the difference.
                  Because of time constraints, not everything in the reading will be discussed in lecture,
                  andnoteverythinginlecturewillbecoveredinthereading. Youareresponsibleforboth.
        All course materials will be posted on Canvas. Check for updates and announcements on a
        regular basis. For ease of grading and to keep an easily accessible record, we will also be using
        Gradescopefor homework this semester instead of paper submissions.
        Office hours will be posted and updated on Canvas in Calendar. If your schedule keeps you
        away from office hours, let us know. We can either adjust the schedule or make separate
        appointments, which can be scheduled at the discretion of your instructor. You are welcome to
        get help on homework problems and other questions during office hours.
        Ed Discussion has been setup for the course. Here, you can ask (and answer) anonymous
        and questions about course material, such as questions about lecture or homework problem,
        ask for clarifications, and discuss with instructors and fellow students. The advantage of Ed
        Discussion is that everyone in the course can see the public questions and answers, so the
        questions only needs to be asked once, and other students can answer your questions or add
        follow-up comments. You can also ask private questions if you prefer.
        PreceptswillbeheldonFridaystohelpyouworkthroughproblemsandansweryourquestions.
        At these sessions, you will work with an instructor though several problems as a class, as well
        as working together in small groups. Some of the problems done at these sessions may be
        homeworkproblems, such as those from exam preparation assignments.
        Assignments
        There will be two types of written assignments.
        Problem sets from the textbook will be posted weekly on Canvas and must be turned in on
        Tuesdays by 11:59 pm Princeton time, with a few exceptions throughout the semester. Note,
        textbookproblemsaremeanttointroduceyoutothematerialandaremorestraightforwardthan
        examproblems. All problem numbers are from the 14th edition of the book.
        Exampreparationassignmentsaredesignedtohelpyouprepareforexams. Therewillbefour
        such assignments, one due each week before an in-class exam. They will be due on Fridays,
        also by 11:59 pm Princeton time.
        Late submissions will not be accepted. The only exceptions are a serious illness with a
        doctor’s note or an emergency communicated through the Dean’s office. However, the the
        lowest scoring problem set will be dropped.
        Youareencouragedtoworktogetherwith your classmates on the problem sets, but you must
        write up your own solutions in your own words. Please scan your work legibly, write in clear
        sentences, circle answers whenever appropriate, and record the names of your collaborator(s).
        Youmaylosepointsforunclearworkorpoorscans. Keepinmindthatdirectly copying solutions
        fromanotherstudent,fromasolutionsmanual,orfromtheinternetisawasteofeveryone’stime,
        as well as a violation of the expected standard of academic integrity. Please carefully read the
        AcademicIntegrity Policy posted in Modules on Canvas.
                    Gradescopewillbeusedtosubmitallassignments. Makesureyouwritelegibly,circleanswers,
                    use complete sentences when appropriate, and record the names of your collaborator(s) form
                    outside of precept and office hours. You may lose points for unclear work or illegible scans.
                    Examinations
                    There will be four in-class exams during the semester, followed by a cumulative final exam.
                    Exam2willtakeplacein-class during midterm week on Wednesday October 13, while all other
                    in-class exams will take place on Fridays instead of precepts. Note, we will have a lecture with
                    newmaterial on the Monday of midterm week.
                                                   Exam1 September16
                                                   Exam2 October13
                                                   Exam3 November12
                                                   Exam4 December3
                                                       Final   WeekofDecember15-21
                    Eachin-class exam will be 50 minutes, test new material, and take place during your scheduled
                    precept. The details and time of the final exam will be announced later.
                    Grading
                    The final course grade will be determined according to your performance as follows
                                               15% Problemsetsafter lowest one dropped
                                               10% Fourexampreparation assignments
                                               40% Fourin-class exams
                                               35% FinalExam
                    ODSAccommodations
                    Testing and other accommodations are assessed and authorized by the Office of Disability
                    Services. Anaccommodationcannotbeimplementedwithouttwothings: (1)approvaldirectly
                    from ODS in advance and (2) direct contact from the student. As soon as possible, please
                    contact your instructor and the course heads if you have approved accommodations.
                Tentative Schedule
                Below is a tentative schedule of lectures and exams. Friday precepts are not listed as they will
                focus on the material from the previous two or three lectures. Note, there will not be precepts
                on September 3 and October 15.
                 Lectures      Dates      Topics
                    1           9/1       3Dspaceandquadricsurfaces
                                          Sections 12.1, 12.6
                     *          9/3       Noprecept
                    2           9/8       Vectors, dot and cross products, projections
                                          Sections 12.2 – 12.4
                    3          9/13       Lines, planes, and distances
                                          Section 12.5
                    4          9/15       Curves in space and parametrization
                                          Section 13.1
                    5          9/20       Projectile motion and arclength
                                          Sections 13.2 – 13.3
                    6          9/22       Functions of several variables, limits, and differentiation
                                          Sections 14.1 – 14.3
                  Exam1        9/24       Sections 12.1–12.6
                    7          9/27       Chain rule and implicit differentiation
                                          Sections 14.4
                    8          9/29       Directional derivatives, tangent planes and gradient
                                          Sections 14.5 – 14.6
                    9          10/4       Critical points and extreme values
                                          Section 14.7
                    10         10/6       Lagrange Multipliers
                                          14.8
                    11         10/11      Taylor Polynomials
                                          Section 14.9
                  Exam2        10/13      Sections 13.1-13.3 and 14.1-14.8
                     *         10/15      Noprecept
                   Break   10/16 – 10/24  Fall Recess
                    12         10/25      Double Integrals in Cartesian coordinates
                                          15.1–15.2
                    13         10/27      Area using double integrals and polar coordinates
                                          Sections 15.3 –15.4
                    14         11/1       Triple Integrals and applications
                                          Sections 15.5–15.6