Vector Calculus (MTH 3035), Spring 2024 (2nd 7 weeks)
Instructor: Andrew Obus
Email: Andrew.Obus [at] baruch.cuny.edu Office: VC 6-223
Office phone: 646-312-4008
Website: http://faculty.baruch.cuny.edu/aobus
Office hours: Mondays 2:15 – 3:15 (in person), Tuesdays 11:00 – 12:00 (on Zoom).
Lectures: Wednesdays, 9:55 – 11:35, VC 4-220, starting March 20.
Lectures
Please ask questions if anything in lecture is unclear.
Attendance and class participation are crucial for learning the
material for this course. We have only 8 class sessions to learn a great deal of material. Furthermore, quizzes will take place at the beginning of class (see below), so it is imperative that you show up on time!
CELL PHONES MAY NOT BE TAKEN OUT DURING CLASS! If you know that you are expecting an important call (relative in the hospital, etc.), you must let me know ahead of time. Phones in class are extremely distracting to you, to me, and the people around you, and they are detrimental to your understanding of the material. I will stop class to ask you to put them away, and repeated cell phone use can count against your grade in borderline situations (see “Final Course Grades”).
This course will not require a calculator, although we may make use of some online computing/drawing software in class and on the homework. Calculators will not be permitted on exams.
Textbook
Calculus, 11th Edition, by Ron Larson and Bruce Edwards. This is the same book that was used in MTH 3020/3030.
The eBook is bundled together with your WebAssign access. The instructions are in an announcement on Blackboard. Note that if you have taken a previous calculus course at Baruch you should have multi-term access to WebAssign already and should not have to make a purchase.
Content
This course is dedicated to various generalizations of the fundamental theorem of calculus in 2 and 3 dimensions. Unlike in MTH 3020/3030, where you studied functions with multiple inputs and one output, this course will focus on functions with multiple outputs, called “vector-valued functions”. These functions are well-adapted to measuring motion in space, as well as gravitational, magnetic, and electric fields. The material here is a beautiful unification of geometry and calculus, and is also extremely useful in physics and engineering.
In particular, we will cover the first bit of Chapter 12 and most of Chapter 15 in the book. As you know by now, math is very cumulative. So if you fall too far behind in this course, it will be difficult to catch up. Please see me promptly if things stop making sense!
This course is extremely fast-paced, and there will not be much time for review of prior material. So if you have time before class begins in late March, it would be a good idea to review material from MTH 3020/3030, especially the material on double and triple integrals, which will be used liberally throughout this course.
The “official” departmental syllabus for MTH 3035 (including a list of relevant problems from the text), along with its Learning Goals, is available here.
Prerequisite: MTH 3020/3030 with a grade of B+ or better.
Office Hours
Mondays 2:15 – 3:15 (in person, VC 6-223), Tuesdays 10:30-11:30 (on Zoom). I am also happy to make a Zoom appointment with you at some other time if you prefer. I want to make sure you can succeed in this class!
Homework and Quizzes
Homework will be assigned every week, both written and on WebAssign. For the WebAssign problems, you will in general have 9 attempts to answer the question, but the numbers in the question will change after every 3 attempts. WebAssign problems are due on Wednesdays at 5:00 PM. Written homework is due by the end of office hours after class on Wednesdays (12:35 PM). Late homework will not be accepted, but your lowest written homework score and your lowest WebAssign score will be dropped.
There may occasionally be an extra credit homework problems assigned. Such a problem will usually require some ingenuity!
You are encouraged to discuss homework with your classmates, but you must write up the actual problems on your own.
There will be a short (10 minute) in-class quiz most Wednesdays inspired by (or drawn directly from) the WebAssign homework, given at the beginning of class. This is to ensure that you are actually doing and understanding the homework. The quiz ends at the same time for everyone, regardless of when you show up! There are no make up quizzes, but your lowest quiz score will be dropped.
Exams
This class does not have a midterm exam. The only exam is the final, which will take place Monday, May 20 from 10:30 – 12:30, room TBA. Exam questions will require written answers (no multiple choice or fill-in-the-blanks). Partial credit will be given for correct work shown.
Final Course Grades
15% Written Homework
15% WebAssign Homework
20% Quizzes
50% Final Exam
Grading will be based on the Baruch grading scale. It is possible for exceptional class participation to be factored into your numerical grade in borderline cases.
Academic Honesty
Any cheating on exams, quizzes, or homework will result in a grade of 0 on the assignment involved. A second instance of cheating will result in automatic failure of the class. Refer here for more information on Academic Honesty.
Extra Help
The textbook comes with free access to CalcView.com and CalcChat.com. CalcView has video solutions for some exercises in the book, and CalcChat has written solutions to many odd-numbered exercises, plus access to online tutors.
Disabilites
All students with special needs requiring accommodations should present the appropriate paperwork from Student Disability Services. It is the student’s responsibility to present this paperwork in a timely fashion and follow up with the instructor about the accommodations being offered. Accommodations for test-taking (e.g., extended time) should be arranged at least 5 business days before an exam.
Schedule (topics subject to change)
| Class # | Date | Topics | Book Sections (approximate) | Remarks |
| 1 | 3/20 | Introduction to vector-valued functions | 12.1, 12.2 | |
| 2 | 3/27 | Calculus on vector-valued functions, vector fields | 12.2, 15.1 | Quiz 1, HW 1 Due |
| 3 | 4/3 | Line integrals | 15.2 | Quiz 2, HW 2 Due |
| 4 | 4/10 | Conservative vector fields, independence of path, Green’s theorem | 15.3, 15.4 | Quiz 3, HW 3 Due |
| 5 | 4/17 | Parametric surfaces, surface integrals | 15.5, 15.6 | CLASS ON ZOOM! NO QUIZ HW 4 Due |
| 6 | 5/1 | Continuation of surface integrals, divergence theorem | 15.6, 15.7 | Quiz 4, HW 5 Due |
| 7 | 5/8 | More divergence theorem, Stokes’s Theorem | 15.7, 15.8 | Quiz 5, HW 6 Due |
| 8 | 5/15 | Catch-up, Review | Quiz 6, HW 7 Due | |
| 9 | 5/20 | FINAL EXAM | FINAL EXAM | FINAL EXAM |