Lecture times: MWF 8:00 9:15 OR 2:30 3:20 Lecture location: Greenlaw 101 OR Phillips 215 Instructor: Linda Green Email: greenl@email.unc.edu Office hours: M 4:00 5:00, Tu 1:00 2:00, W 4:00 5:00, Th 3:00 4:00, F 10:00 11:00, and by appointment. Note: Students can attend the office hours of ANY Math 233 instructor. See Piazza for updates to office hours. Recitations: Tuesdays or Thursdays Recitation locations: Phillips 206, 224, 332, 383 Recitation TAs: Russell Arnold, Andrew Ford, Yuan Gao, Marc Besson TA email: rvincent@live.unc.edu, agford@live.unc.edu, gaoyuan@live.unc.edu, marmarc@live.unc.edu Course website: see Sakai Materials: Textbook: Calculus: Early Transcendentals, (or Multivariable Calculus) by Stewart, 8th Edition. Your copy needs to include chapters 12 16. Access to an e-book comes with access to WebAssign. WebAssign: You will need access to WebAssign for homework. If WebAssign did not come with your textbook, you need to purchase it separately. See the information on homework below. Poll Everywhere: You will need to register for Poll Everywhere to answer questions in class using your cell phone or laptop. See the instructions below. Piazza: Please use Piazza instead of email to ask questions about homework problems and logistics. Other students and the instructor can answer them there for the benefit of all students. See details below. Calculator: You will need a basic scientific calculator. I recommend a graphing calculator (e.g. TI-84 or TI-89) for visualizing functions and checking answers. Calculators will not be permitted on tests or quizzes unless otherwise specified. Calculators will not be permitted on the final exam. 3-Dimensional Graphing Apps: Wolfram Alpha and the Mac Grapher app are easy to use to help visualize surfaces and other objects and to check computational problems. UNC students can download a free copy of Mathematica for more sophisticated graphs and computations. See the resource list on Sakai. Other: Supplementary materials will be posted on the course website on Sakai. Videos are on the instructor s YouTube channel and links to the videos are posted on Sakai. Prerequisites: In order to be eligible to register for this course, AT LEAST ONE of the following must be true: You earned at least a 3 on the AP Calculus BC exam. You earned at least a 5 on the IB High Level exam. You passed Math 232 at UNC-CH, or have the equivalent transfer credit (C or above for transfer credit). You have placement credit for Math 232 based on the Math Department s Calculus Placement Test. Course Description: Math 233 is a course in multivariable calculus that extends the ideas of differentiation and integration to functions of two or more input variables and to vector-valued functions that whose output is in two or more dimensions. This course covers parts of Chapters 12 through 16 of the textbook. At the end of this course, students should be able to: Use vectors, dot product, and cross-product to solve problems in physics and geometry Write equations for lines and planes in three dimensions Use vector equations to describe curves in space Analyze limits and continuity for functions of two variables Find partial derivatives of functions of two and three variables Compute and interpret directional derivatives and the gradient Use linearization (the tangent plane) to approximate functions of two variables Optimize functions of two or three variables Compute double and triple integrals, changing the order of integration when appropriate Compute double integrals using polar coordinates and compute triple integrals using spherical coordinates Compute line integrals of functions and vector valued functions 1
Explain multiple ways to determine if a vector field is conservative Use Green s theorem to rewrite double integrals as single integrals and vice versa Parametrize surfaces Compute surface area and surface integrals Compute and estimate divergence and curl Use the Divergence theorem and Stokes theorem to rewrite and compute integrals Class Structure: Students are expected to prepare for each MWF class by reading the text and / or watching assigned videos, and then completing a short pre-class assignment on WebAssign. The pre-class assignments are due by 8:00 am. Classes on MWF will be lectures. The instructor will post a skeleton version of the notes on Sakai before each class and a filled in copy of the notes after class. During the Tuesday or Thursday recitations led by the TAs, students will solve problems on topics related to the current lectures and homework. Homework: Please refer to the schedule on WebAssign for homework due dates. Please refer to the instructions below to set up your WebAssign account. Your lowest homework score will be dropped if at least 80% of students complete the mid-semester course evaluation. Your second lowest homework score will be dropped if at least 80% of students complete the course evaluation at the end of the term. Pre-class assignments: There will be pre-class WebAssign assignments for most classes, due at 8:00 am.. Your scores on the pre-class assignments will be included in your homework grade. The lowest two scores on pre-class assignments will be dropped. Regular homeworks will be weighted 10 points and pre-class assignments will be weighted 2 points towards the total WebAssign grade. Website: https://www.webassign.net/login.html Class Key: unc 3585 0884 Users New to WebAssign at UNC Click on I have a Class Key. Enter the appropriate class key from above and submit. Verify that you have the correct class and choose Need to Create Complete all boxes with an * beside them with your personal information. Click on Create my account. Click on Log in. From this point on you will sign in as a returning user with your User Name, Institution (unc), and Password. You have a 14 day grace period before you need to enter your access code or purchase one from WebAssign. Previous Users of WebAssign at UNC Click on I have a Class Key. Enter the appropriate Course Key from above and submit. Verify that you have the correct class and choose Already Have You can log in with your User Name, Institution (unc), and Password. You have a 14 day grace period before you need to enter your access code or purchase one from WebAssign. Poll Everywhere Questions: During lecture, the instructor will ask questions for all students to answer using Poll Everywhere on their phones or laptops. A student s participation score for a class period will be the percentage of Poll Everywhere questions that the students answers during that class period. Points are awarded for participation only, with no deduction for incorrect answers. The lowest 4 participation scores will be dropped. 2
In order to get credit for answers, students need to register for Poll Everywhere through UNC s service at poll.unc.edu. Be sure to go through UNC s website listed above and do NOT sign up directly at polleverywhere.com. There is no charge for students to use Poll Everywhere, but students will need to bring a phone with texting ability or a laptop to class. Students who have registered for Poll Everywhere previously for another UNC course since August 6, 2018 do not need to register again for this course. Piazza: Instead of emailing the instructor or the TAs directly with questions about homework problems or logistics, please post your questions on Piazza. Other students, instructors, and TAs can answer them there for the benefit of all students. If you were not already automatically added to Piazza, you can register yourself here: piazza.com/unc/fall2018/math233. The Piazza site will be used by all sections of Math 233. Recitation Problems: Students will be assigned to groups to work on problems in recitation. Students will be graded for participation, and one solution per group will be graded for the quality of the solution, based on its accuracy, completeness, and clear exposition. Each student s grade will be the sum of their individual participation score and their group s quality score. Recitation problem scores and quiz scores will be pooled together into one grading category and the lowest two scores in this category will be dropped. Tests and Quizzes: There will be a quiz given some weeks. Usually, the quiz will be given during recitation. Sometimes, the quiz may be online through WebAssign. Quiz topics and format will be announced in advance during the lecture or posted on Sakai. Your quiz scores and recitation problem scores will be pooled together into one grading category, and the lowest two scores in this category will be dropped. There will be two tests during the semester. Their tentative dates are as follows: Test 1: 9/28/18 Test 2: 11/16/18 No make-up tests or quizzes will be given. Tests or quizzes can be given early only if the student will be absent for university athletics, an academic field trip, or a religious holiday and makes prior arrangements with written documentation at least a week in advance. The grade on the final exam will be used to replace either a missing test grade or the lowest test grade if the final exam score is higher. The comprehensive final exam will be on Friday, Dec. 7, 8:00 11:00 AM. The final exam is given in compliance with UNC s final exam regulations and calendar, and will not be given prior to this exam date. In order to take the make-up exam after this date, you must have an official examination excuse, signed by a Dean or authorized agent of the Dean (in Steele Building). You must bring this excuse, along with a picture ID, to the make-up exam. Grading: All grades will be assigned according to a 10-point scale. That is, 93 100 is A, 90 92 is A-, 87 89 is B+, 83 87 is B, 80 82 is B-, etc. Your course grade will be determined as follows: Participation: 2% Quizzes and Recitation Problems: 8% WebAssign: 12% Tests: 40% Final Exam: 38% Late work: No late work will be accepted for tests, quizzes, or recitation problems. You will be able to get an automatic extension on WebAssign for a ~20% penalty on unanswered questions. 3
Honor Code: It is expected that each student in this class will conduct him or herself within the guidelines of the UNC Honor System, described at http://studentconduct.unc.edu/students. In this class, all quizzes, tests, and exams must be done individually and are closed book and closed notes unless otherwise specified. It is an instance of cheating to give or receive help on a quiz, test, or exam, except from the instructor. On homework assignments, pre-class assignments, and recitation assignments, students are encouraged to work together in pairs or small groups, provided that all participants are contributing and the collaboration benefits the learning of all involved. Simply copying or trading answers is an instance of cheating. On in-class problem solving assignments, students are encouraged to work together unless otherwise specified. If you are not sure if collaboration is permitted, please ask! In addition to avoiding actual academic dishonesty, please avoid appearances of academic dishonesty. In particular, please silence and put away cell phones before any exams are handed out and please avoid the appearance of looking at other students papers. In order to maintain a proper testing atmosphere, the instructor may ask students to switch seats before or during an exam. Students who observe a violation of the honor code should report it to the instructor. The instructor will report any suspected honor code violations to the Student Attorney General. Additional Resources: The Math Department sponsors free tutoring in the Math Help Center in 237 Phillips Hall. Hours are typically M Th 10 6 and F 10-3. See http://math.unc.edu/for-undergrads/help-center for schedule updates and other details. You can go to the office hours of any instructor teaching 233 see list of office hours on Piazza TAs will hold office hours M and W from 5 6, room TBD. Free tutoring is available on the second floor of Dey Hall on Tues. and Wed. evenings from 6 9 pm. The Math Department keeps a list of paid tutors in the main office in Phillips 329 and online on the Math Department website. Copies of final exams from previous years will be available on Piazza and / or Sakai and / or the Math Department website. The Learning Center has a math coach who can give you tips on how to study for and succeed in a math class. Disclaimer: The instructor reserves the right to make changes to the syllabus, including due dates and test dates. Changes to WebAssign due dates can be found on the WebAssign site. Other changes will be announced in class or on Sakai or via Piazza. 4
TENTATIVE SCHEDULE OF INSTRUCTION WEEK DATES SECTION 1 8/22 8/24 Syllabus 12.1: 3D coordinates 12.6: Quadric surfaces 12.2: Vectors 2 8/27 8/31 12.3: Dot product 12.4: Cross product 3 9/3 9/7 12.5: Equations of lines and planes 13.1: Vector Functions and space curves 4 9/10 9/14 13.2: Derivatives and integrals of vector functions 14.1 Functions of several variables 14.2 Limits and continuity 5 9/17 9/21 14.3 Partial derivatives 6 9/24 9/28 14.4 Tangent planes and linear approximations 14.5: Chain rule 14.6: Gradient and directional derivatives Test 1 on 12.1-12.6, 13.1 13.2, 14.1 14.4 9/28 7 10/1 10/5 14.7 Optimization 14.8 Lagrange Multipliers 8 10/08 10/12 15.1: Double integrals over rectangles 15.2: Double integrals over general regions 15.3: Double integrals in polar coordinates 9 10/15 10/19 15.4 Applications of double integrals 15.6 Triple Integrals Fall Break 10 10/22 10/26 15.7 Cylindrical Coordinates 15.8 Spherical coordinates 16.1 Vector fields 11 10/29 11/2 16.2 Line integrals 16.3 Fundamental Theorem of Line integrals 12 11/7 11/10 16.4: Green s Theorem 16.5 Divergence and Curl 13 11/12 11/16 11/16 16.6 Parametric surfaces and surface area Test 2 on S14.5 14.8, 15.1 15.8, 16.1 16.5 14 11/19 16.7 Surface integrals Thanksgiving 15 11/26 11/30 16.8 Stokes Theorem 16.9 Divergence Theorem 16 12/3 12/5 Catch up and review 12/7 FINAL EXAM Friday, Dec. 7 from 8:00 am 11:00 am Notes: 1) This schedule may be changed. The instructor will notify students of any changes. 2) WebAssign homework assignments are due by 11:59 PM on the due date posted on the WebAssign. WebAssign pre-class assignments are due at 8:00 am on the day that the material is first covered. Login to WebAssign to see what is due when. 5