MATH 3404 Multivariate Calculus (Honors Section) Fall 2018 Instructor: Dr. Scott M. LaLonde Office: RBN 4005 Phone: (903) 565-5839 (Math department main office) Email: slalonde@uttyler.edu (preferred method of contact) Office hours: Tuesdays and Thursdays 3 4 p.m., Wednesdays 2 3 p.m., or by appointment. Scheduled lectures: Section 029 MWF, 10:30 a.m. 11:45 a.m. Location: RBN 4039 Course Webpage: All course information and documents will be available on Canvas. Textbook: Essential Calculus: Early Transcendentals, Second Edition, by James Stewart. (ISBN: 978-1-133-11228-0) Prerequisites: A grade of C or better in Calculus II (MATH 2414 or equivalent). Course Description Vector calculus in Euclidean n-space, functions of several variables, partial differentiation and multiple integration. Student Learning Outcomes Upon completion of this course, students should be able to do the following: Use vectors to describe lines, planes, and curves in three-dimensional Euclidean space. Compute velocity, acceleration, curvature, and arc length along curves in space. Apply the operations of calculus to compute limits and derivatives of multivariable functions. Use derivatives to find maxima and minima of multivariable functions in both constrained and unconstrained settings. Set up and compute iterated integrals (i.e., double and triple integrals) of multivariable functions in rectangular, cylindrical, and spherical coordinates. Set up and compute line integrals and surface integrals of vector fields in two- and threedimensional Euclidean space. Use the Fundamental Theorem of Line Integrals, Green s Theorem, Stokes s Theorem, and the Divergence Theorem to simplify the computation of line and surface integrals. Solve assorted real-world problems using all the techniques of multivariable calculus. 1
Assignments and Grading Online Homework Practice problems will be assigned daily via the online platform WeBWorK. You can access the homework assignments by going to the following link: http://math.uttyler.edu/webwork2/m3404_hnrs_fall2018/ Your WeBWorK username is the same as your Patriots username. (For example, if your Patriots email is jdoe@patriots.uttyler.edu, your username is jdoe.) Your initial password is set to your student ID number I recommend that you change it immediately once you log in for the first time. WeBWorK accounts will be activated shortly before the first day of classes. A more detailed guide to using WeBWorK will be available on Canvas as well. In general, a new homework assignment will become available on WeBWorK after each class. Many problems will be similar to ones we ve done in class, but some will require additional thought. The assignment will be due by 10:00 a.m. (i.e., shortly before class) two class days later. The WeBWorK system provides you with instant feedback on your answers, as well as unlimited attempts to complete most problems. You should use this to your advantage and do each assignment. When computing your final grade, I will use your total score on all the WeBWorK problems. For example, if there are a total of 150 problems throughout the semester, and you complete 120 of them, your homework grade will be 80%. In-class Activities A large portion of our class time will be devoted to discussion, participation, and group work. In particular, there will be regularly scheduled days throughout the semester (usually on Wednesdays) where much or all of the class period is devoted to some kind of group exercise. You will work together with some of your classmates to further explore the course material, usually in one of the following forms: practice problems to help reinforce the material and build problem-solving skills; mini-projects designed to explore concepts or study applications of the current material. Some in-class assignments may result in short homework assignments that are due before the next class. (That is, if you do not complete a worksheet in class, you might have the opportunity to finish it later.) At the end of each activity, some of you may be asked to present certain problems to the class. Your participation in these activities will contribute to your overall grade in the course. I will collect your work from that day and more or less check it for completion, and I will also assess your presentation of problems. Your grade might also depend in part on your participation during in-class discussions and any potential quizzes or homework (if those things become necessary). Exams There will be three exams during the semester, as well as a comprehensive final exam. All exams will be held in class with no books, notes, or calculators allowed. The tentative dates are: Exam 1: September 19 2
Exam 2: October 17 Exam 3: November 14 Final Exam: December 12, 10:15 a.m. 12:15 p.m. (Location TBD) Grading Your grade will be computed as follows: Assignment Total % WeBWorK 5 In-class activities 15 Written homework 5 Exams 15% 3 = 45 Final exam 30 Total 100 Numerical Letter 90 100 A 80 89 B 70 79 C 60 69 D Below 60 F All assignments will count when computing your final grade. In particular, I will not drop or replace your lowest exam grade. There may be occasional chances to earn bonus points via homework assignments or in-class participation, but you should not expect a significant amount of extra credit in this course. Course Policies Canvas You must activate your Canvas account and check it regularly. You can activate your account and log in at https://www.uttyler.edu/canvas. If you are registered for the course, then you should already have access to the Canvas page. All announcements and important documents will be posted there. Email In addition to Canvas, the preferred means of communication for this course is official UT Tyler email. If you email me, it needs to be sent from your Patriots account to my UT Tyler email address (slalonde@uttyler.edu). As a test, send me a picture of Admiral Ackbar with the subject It s a trap! once you ve finished reading this syllabus. In the event that I need to contact you, I will send an email to your Patriots account, and I will assume that you have read any such message. Office Hours I have regularly scheduled office hours, which are set aside as time for you to come talk to me about the course. This should be your first course of action if you find that you are struggling. You should not be afraid to come ask me questions when you are studying or working on homework. This course moves quickly don t let yourself fall behind. If you are unable to attend my usual office hours, you can always set up an appointment or ask questions via email. 3
Attendance I expect you to attend class every day. Attendance is not officially part of your grade, but poor attendance will affect your grade both directly (through your participation grade) and indirectly (by impacting your performance on exams). This class moves quickly, so it will be quite difficult for you to succeed in this course if you are repeatedly absent from class. In the event that you do miss class, you are responsible for catching up on the material that was covered that day. You are also responsible for any announcements made in class. Make-up Policy Make-ups will only be granted for excused absences that are required as part of a UT Tyler obligation, or for religious observances. You must notify me at least one week ahead of time and provide appropriate documentation. Other makeups are granted only in extreme cases and at the discretion of the instructor. Makeups will not be granted after the fact under any circumstances. Mathematics Learning Center (MLC) The math department hosts a drop-in tutoring center located in RBN 4021. It is staffed by mathematics graduate students, as well as some advanced undergraduates. It will be open most days throughout the semester, starting with the second week of classes. The MLC is an excellent resource for obtaining extra, on-demand help with your lower-level math classes. While Math 3404 is not one of the official classes supported by the MLC, the graduate student tutors are certainly capable of assisting you with multivariable calculus. Cell Phones, Calculators, and Electronic Devices When class is about to begin, place any electronic devices (cell phones, MP3 players, etc.) in silent mode and put them out of sight. You may use a laptop or tablet to take notes or consult the textbook (if you ve purchased the electronic version). If you are using these devices for other purposes, I will ask you to put them away. Calculators of any kind are not allowed on exams. Plagiarism and Academic Dishonesty Any work you submit must represent your own effort. If I determine that this is not the case, I will prosecute plagiarism and academic dishonesty to the fullest possible extent. In particular: All exams are closed book, with no books, notes, or calculators allowed. No help will be given or received. You may not use online calculators (such as WolframAlpha, Symbolab, Mathway, etc.) to solve WeBWorK problems for you. Entering an answer obtained from one of these services to ensure you get credit for the problem constitutes cheating and will be dealt with accordingly. Changes to Syllabus I reserve the right to make changes to the syllabus during the semester. Any changes to course policies will be announced in class, and an updated version of the syllabus will be posted to Canvas. 4
Important Dates August 27: Classes begin. September 3: Labor Day holiday. No class. September 10: Census date. Last day to change schedule or file for grade replacement. November 5: Last day to withdraw. November 19 23: Thanksgiving break. No classes. December 10: Study day. December 12: Final exam. University Policies Information on University policies concerning the following topics: UT Tyler Honor Code Students Rights and Responsibilities Campus Carry UT Tyler Tobacco-Free Policy Grade Replacement/Forgiveness and Census Date State-Mandated Course Drop Policy Student Accessibility and Resources Student Absence due to Religious Observance Student Absence for University-Sponsored Events and Activities Social Security and FERPA Statement Emergency Exits and Evacuation Student Standards of Academic Conduct UT Tyler Resources for Students can be found at http://www.uttyler.edu/academicaffairs/files/syllabuspolicy.pdf 5
Tentative Daily Schedule This schedule is subject to change as we move through the semester. The section of the textbook listed in the To read column corresponds roughly to the topics that we will cover that day, and it is strongly suggested that you read it before class. Week Date Topics covered To read 1 2 3 4 5 6 7 8 9 10 8/27 Overview of multivariable calculus. The geometry of vectors and Euclidean space. 8/29 The dot product, length, and distance. 10.3 10.1 10.2 8/31 Determinants and the cross product. Planes in R 3. 10.4 10.5 9/3 Labor Day no class. 9/5 In-class project on vectors, lines, and planes. Quadric surfaces. 10.6 9/7 Calculus of space curves. 10.7 9/10 Arc length and curvature. 10.8 9/12 In-class project on space curves. 9/14 Applications to physics: Motion in space. 10.9 9/17 Functions of several variables. 11.1 9/19 Exam 1 9/21 Limits and continuity for functions of several variables. 11.2 9/24 Partial derivatives. 11.3 9/26 Tangent planes and linear approximations. 11.4 9/28 In-class project on derivatives and tangent planes. 10/1 The chain rule. 11.5 10/3 Directional derivatives and the gradient of a function. 11.6 10/5 In-class project on directional derivatives. 10/8 Maxima and minima of multivariable functions. 11.7 10/10 In-class project on maxima and minima. 10/12 Constrained optimization and Lagrange multipliers. 11.8 10/15 Double integrals over rectangles. 12.1 10/17 Exam 2 10/19 Double integrals over general regions. 12.2 10/22 Double integrals in polar coordinates. 12.3 10/24 Applications of double integrals. 12.4 10/26 Triple integrals. 12.5 10/29 Triple integrals in cylindrical and spherical coordinates. 12.6 12.7 10/31 In-class project on triple integrals. 11/2 The change of variables formula for multiple integrals. 12.8 6
11/5 Vector fields. 13.1 11 11/7 Line integrals. 13.2 11/9 The Fundamental Theorem of Line Integrals. 13.3 11/12 In-class project on line integrals. 13.4 12 11/14 Exam 3 11/16 Green s Theorem. 13.4 13 11/19 Thanksgiving break no classes 11/26 Curl and divergence. 13.5 14 11/28 Parametric surfaces. 13.6 11/30 Surface integrals. 13.7 12/3 Stokes s Theorem. 13.8 15 12/5 The Divergence Theorem. 13.9 12/7 In-class project on the Stokes family of theorems 12/12 Final Exam 7