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 (like 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 calculus so you can solve any such problem you encounter in mathematics, the sciences, or engineering, and that requires trying to solve new problems from first principles, if only because the real world is sadly complicated.
Please note there are two versions of this text currently available, and this course uses the 6th edition rather than the 7th. You will also need WebAssign access to do the online homework. The U of I bookstore is selling a bundle of the text and WebAssign for $159, and the same is available directly from the publisher for $140.00 (including shipping). If you buy a used copy, or a new copy without WebAssign, you can purchase single-semester access to WebAssign for $47.
Overall grading: Your course grade will be based on the online HW (10%), section worksheets and quizzes (6%), three in-class 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 be curved more generously depending on their difficulty.
Exams: There will be three evening midterm exams, which will be held from 7:00–8:30pm on September 20, October 18, and November 14 (all Tuesdays).
There will be a combined final exam for these sections of Math 241. The final exam will take place on Tuesday, December 13 from 1:30pm–4:30pm, with the conflict exam on Wednesday, December 14 from 8:00am–11:00am.
All exams will be closed book and notes, and no calculators or other electronic devices (e.g. cell phones, iPods) will be permitted.
Homework: Homework will be assigned for each lecture and posted on the course webpage. Most of this will be done online via WebAssign, and will generally be due two lectures later, just before the 8am class starts. That is, HW for Monday’s lecture is due Friday at 8am, and Wednesday’s is due on the following Monday, etc. The other HW problems you will be responsible for on exams and quizzes but will not be collected. Late HW will not be accepted, but the lowest 5 scores will be dropped. The first assignment is due Friday, August 26.
Homework Solutions: WebAssign lets you see a complete solution to any assigned problem once the due date has passed. For the other HW problem, you can check your answers and see the solutions here: Part 1, Part 2, Part 3, Part 4.
WebAssign: To sign up for the online HW, go to WebAssign and enroll using the Class Key:
Important: Be sure to provide your NetID@illinois.edu address when WebAssign asks for your email. This is crucial for your HW scores to be credited toward your grade. Technical issues with WebAssign should be addressed here. If you have not yet received your WebAssign access code, sign up for the 14 day free trial so you can start doing the HW immediately.
Worksheets and Quizzes: Most section meetings will include either a worksheet or a quiz. The former will be graded for effort and latter for accuracy. Missing either results in a score of zero, but the lowest 4 scores in this category will be dropped.
Conflict exams: If you have a conflict with one of the exam times, please consult the university policy on evening midterm exams and final exam conflicts. Based on that, if you think your situation qualifies you to take the conflict exam, please contact me as soon as possible, but no later than a week before the exam in question. I reserve final judgment as to which exam you will take.
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 by an absence letter from the Emergency Dean located in Room 300 of the Turner Student Services Building, though I reserve final judgment as to whether an exam will be excused. All requests for an exam to be excused must be made within a week of the exam date.
Missed HW/worksheets/quizzes: 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.
Exam Regrading: The section leaders and myself try hard to accurately grade all exams and quizzes, but please contact one of us if you think there was an error. All such requests for regrading must be made within one week of the test being returned.
Viewing grades online: You can always find the details of your worksheet, quiz, and exam scores here. Due to a limitation of the system, both worksheets and quizzes are recorded as "qu". Details of your HW scores can be viewed on WebAssign, and are only periodically input into the above system as an overall average (hw).
Large-lecture Etiquette: Since there are more than 200 people in the room, it’s particularly important to arrive on time, remember to turn off your cell 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. 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 to should see 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.
James Scholar/Honors Learning Agreements: These are not offered for this section of Math 241. Those interested in such credit should enroll in one of the honors sections of this course.
Ask questions in class: This applies to both the main lecture and the sections. The lecture may be large, but I still strongly encourage you to ask questions there. If you’re confused about something, then several dozen other people are as well.
Come to office hours: I have office hours from Monday 1:30-3:30, Tuesday 9:30-10:30, and Thursday 2:00-3:30 in 378 Altgeld. If those times don’t work for you, you can make an appointment by sending me email or talking to me after class.
Math 241 tutoring room: Come and work with the TAs and your classmates on homework, test preparation, and any general questions about Math 241:
Other sources: A change of perspective is sometimes helpful to clear up confusion. Here are two other vector calculus sources you might find helpful. They are both on reserve at the Math Library in Altgeld Hall: