The focus of this course is vector calculus, which concerns functions of several variables and functions whose values are vectors rather than just numbers. In this broader context, we will revisit notions like continuity, derivatives, and integrals, as well as their applications (such as finding minima and maxima). We’ll explore new geometric objects such as vector fields, curves, and surfaces in 3-space and study how these relate to differentiation and integration. The highlight of the course will be theorems of Green, Stokes, and Gauss, which relate seemingly disparate types of integrals in surprising ways.
For most people, vector calculus is the most challenging term in the calculus sequence. There are a larger number of interrelated concepts than before, and solving a single problem can require thinking about one concept or object in several different ways. Because of this, conceptual understanding is more important than ever, and it is not possible to learn a short list of “problem templates” in lecture that will allow you to do all the HW and exam problems. Thus, while lecture and section will include many worked examples, you will still often be asked to solve a HW problem that doesn’t match up with one that you’ve already seen. The goal here is to get a solid understanding of vector calculus so you can solve any such problem you encounter in mathematics, the sciences, or engineering. That requires trying to solve new problems from first principles, if only because the real world is sadly complicated.
This is an honors course. As a formal matter, this means your grade will have an "H" after it on your transcript and it can help you maintain James Scholar status. As a practical matter, I'll treat the material in a little more depth and from a somewhat more sophisticated viewpoint than the regular sections of Math 241. You'll also do some more work, in the form of the honors homework assignments discussed below. I basically view this class as ordinary Math 241 plus 15% more mathy goodness for those who particularly enjoy the subject.
Please note that this course uses the 9th edition rather than the 8th. You will also need WebAssign access to do the homework. For complete information on purchasing options for both, see https://go.illinois.edu/calculus. If you have the standard text and WebAssign package from Math 220, 221, or 231 from last year, then you already have everything you need for this course. Even before you purchase WebAssign, you can freely use it for the first two weeks of class and so not miss any homework assignments. Several physical copies of the textbook are on reserve at Grainger Library.
Overall grading: Your course grade will be based on the online HW (7%), honors HW (4%) section worksheets (5%), three midterm exams (18% each), and a comprehensive final exam (30%). Grade cutoffs on any component will never be stricter than 90% for an A– grade, 80% for a B–, and so on. Individual exams may have grade cutoffs set more generously depending on their difficulty.
Exams: There will be three midterm exams, which will be held in class September 23 (Monday), October 18 (Friday), and November 15 (Friday). The final exam will be held Wedneday, December 18, from 7pm–10pm.
All exams will be closed book and notes, and no phones, calculators, or other electronic devices will be permitted; where indicated, all work must be shown to receive any credit on a problem.
Online Homework: Online homework will be assigned for each lecture, and will generally be due two lectures later, just before class starts at 1pm. That is, HW based on Monday’s lecture is due Friday at 1pm, and Wednesday’s is due on the following Monday, etc. The homework will be completed online via WebAssign. Late homework will not be accepted, but the lowest 4 scores will be dropped. The first assignment is due Friday, August 30. To access WebAssign, login in to our course's Canvas page (https://canvas.illinois.edu) and click the WebAssign link. You may need to wait 24 hours after registering for the course to be able to log in to WebAssign. For technical problems, contact WebAssign student support; for questions or concerns about HW grades, talk to your TA.
Honors Homework: There will be four honors homework assignments. These consist of more extended and in-depth problems than the the online HW, and will be turned in on paper at the beginning of the corresponding discussion or lecture class. The lowest score in this category will be dropped.
Worksheets: Most section meetings will include a worksheet which will be graded for effort and participation. Missing a worksheet results in a score of zero, but the lowest 3 scores in this category will be dropped.
Missed exams: There will be no make-up exams. Rather, in the event of a valid illness, accident, or family crisis you can be excused from an exam so that it does not count toward your overall average. Such situations must be documented and I reserve final judgment as to whether an exam will be excused. All such requests should be made to me in advance if possible, but in any event no more than one week after the exam date.
Missed HW and worksheets: Generally, these are taken care of with the policy of dropping the lowest scores. For extended absences, these are handled in same way as missed exams.
Regrading: The section leaders and myself try hard to accurately grade all exams, worksheets, and HW, but please contact your TA if you think there is an error. All requests for regrading must be made within one week of the item being returned.
Viewing grades online: You can always find the details of your worksheet and exam scores here. Details of your HW scores can be viewed on WebAssign, and are only periodically input into the above system as an overall average.
Lecture Etiquette: Since there almost 100 people in the room, it’s particularly important to arrive on time, remember to turn off the ringer on your phone, refrain from talking, not pack up your stuff up until the bell has rung, etc. Otherwise it will quickly become hard for the other students to pay attention.
Cheating: Cheating is taken very seriously as it takes unfair advantage of the other students in the class, and is handled as per Article 1 Part 4 of the student code. Penalties for cheating on exams, in particular, are very high, typically resulting in a 0 on the exam or an F in the class.
Disabilities: Students with disabilities who require reasonable accommodations should contact me as soon as possible. In particular, any accommodation on exams must be requested at least a week in advance and will require a letter from DRES.
Conflict final: If you have a conflict with the final exam time, times, please consult the university policy on final exam conflicts. Based on that, if you think your situation qualifies you to take the conflict exam, email me at least one week before the exam date. You will need to provide documentation as to the nature of your conflict, and I reserve final judgment as to which exam you will take.
Ask questions in class: This applies to both the main lecture and your discussion section. The lecture may be large, but I still strongly encourage you to ask questions there. If you’re confused about something, then at least a dozen other people are as well.
The Math 241 tutoring room: Come and work with the TAs and your classmates on homework, test preparation, and any general questions about Math 241 on any Monday, Tuesday, Wednesday, and Thursday from 4pm–8pm in 147 Altgeld. The tutoring room will be staffed starting Wednesday, August 28. Note: this tutoring room is primarily for the regular Math 241 content; questions about the honors HW should be directed to Nathan or Wyatt at their office hours.
Come to office hours: I have office hours 378 Altgeld on Tuesdays from 1:30–2:30pm and on Wednesdays from 3:30–4:30pm. If none of those times work for you, you can make an appointment by sending me email or talking to me after class.
Other sources: A change of perspective is sometimes helpful to clear up confusion. Here are two other vector calculus sources you might find helpful: