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 that this course uses the 7th edition rather than the 6th. You will also need WebAssign access to do the homework. If you have the standard text and WebAssign package from Math 220, 221, or 231 for last year, then you already have everything you need for this course. For information on purchasing the text and WebAssign, please see this page.
Overall grading: Your course grade will be based on the online HW (8%), section worksheets (4%) and quizzes (3%), three evening exams (18% each), and a comprehensive final exam (31%). 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 evening midterm exams, which will be held from 6:45–8:00pm on September 18, October 21, and November 18.
There will be a combined final exam for both lectures of Math 241 Section A on December 12, 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 will generally be due at 8:00am the day after the next lecture That is, HW based on Monday's lecture is due Thursday morning at 8am, (Wednesday's is due Saturday, and Friday's on Tuesday). The homework will be completed online via WebAssign. Late homework will not be accepted, but the lowest 3 scores will be dropped. In addition, missed homework may be excused if there is a justifiable reason, supported by a letter from the emergency dean (or, e.g. a coach). The first assignment is due Thursday, August 280. To access WebAssign login here using your U of I netid and password:
Please note that this procedure may differ from your previous experience, and that you many need to wait 24 hours after registering for the course to be able to log in to WebAssign.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 2 worksheet scores and lowest quiz score 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 Mr. Daniel Hockensmith (hockens2@illinois.edu) 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, family crisis, etc. 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 by contacting Prof. Leininger AND Mr. Daniel Hockensmith (hockens2@illinois.edu).
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 the same way as missed exams.
Regrading: The section leaders and I try hard to accurately grade all exams, quizzes, worksheets, and HW, but please contact one of us if you think there is an error. All requests for regrading must be made within one week of the item being returned. Requests should be made to the TA specified on the particular exam webpage linked above.
Viewing grades online: You can always find the details of your worksheet, quiz, and exam scores here. Exams will be recorded as "ex", quizzes as "qu" and worksheets as "pr". Details of your HW scores can be viewed on WebAssign, and will only be included into the above system as an overall average (hw) at the end of the semester.
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 Prof. Leininger as soon as possible. Any accommodation on exams must be requested at least a week in advance and will require a letter from DRES. Contact Prof. Leininger AND Mr. Daniel Hockensmith (hockens2@illinois.edu) to arrange special accommodations.
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 in 366 Altgeld as listed at the top of this page. If those times don't work for you, and you cannot get the help you need from the helproom, you can make an appointment by sending Prof. Leininger an email or talking to him after class.
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, Monday--Thursday 4:00pm-8:00pm and Friday 3pm-5pm in 239 Altgeld The tutoring room will be staffed starting Tuesday, August 26.
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: