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 will 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.
This honors section will delve deeper into the topics of this course. We will discuss proofs of some of the material, introduce abstractions and generalizations of some of the concepts, and spend less time on some of the easier topics. Concretely, we will discuss (1) linear algebra and linear transformations, which will allow us to provide a more natural, and general, notion of derivative. This will bring a more unified discussion of directional derivatives, gradients, derivatives of parametric curves, and jacobians, and also simplify the discussion of the chain rule; (2) curvature of space curves, which will provide the framework for studying the geometry of surfaces in R3; (3) an introduction to differential forms and integration, sufficient to provide a unified discussion of the Fundamental Theorem of Line Integrals, Greens Theorem, the Divergence Theorem, and Stokes Theorem.
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.
There will also be supplementary materials for concepts outside the scope of this text. These will be linked from the course diary.
Please note that this course uses the 8th edition rather than the 7th. 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.
Email and messages: Email should be reserved for information specific to you (questions about a grade you received, a class you will have to miss, etc.) and should be directed to your TA. He will direct you to me if necessary. For mathematical questions, and questions about the course, please use Piazza (but make sure you check the webpage, first!). For questions about WebAssign, first check this webpage (see below), or the departments information page for Calculus (which includes a FAQ). The FAQ includes a WebAssign help email address for general questions/issues with the WebAssign software. For questions about our class specifically, please email Prof. Leininger.
Overall grading: Your course grade will be based on the online HW (8 points), section worksheets (4 points) and quizzes (3 points), three exams (18 points each), and a comprehensive final exam (31 points). 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, though this information will only be used as a guide in assigning grades at the end of the semester.
Exams: There will be three midterm exams, which will be held in class
There will be a final exam for our section on December 21, 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 weekly, and
will generally be due at 8:00am the following Tuesday unless otherwise noted on the assignment.
The homework will be completed online via
WebAssign. Late homework will not be
accepted, as solutions will appear after the deadline.
In addition, missed homework may be excused only if there is a justifiable reason,
supported by a letter from a doctor (or, e.g. a coach), and only in extreme situations. To
account for mild illness and other minor excuses for missing an assignment, the lowest 3 homework scores will be dropped.
The first assignment is due Tuesday, September 5. To access WebAssign login here using your U of I netid and password:
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: Because we are taking exams during class, because we are not taking a combined final exam, and because we have a relatively small class, there should be no conflict exams necessary for this course. Please consult the university policy on evening midterm exams and final exam conflicts. If you believe you have a conflict, please contact the instructor no later than 1 week before the exam.
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 Student Assistance Center located in Room 300 of the Turner Student Services Building or a letter from a doctor, 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 the instructor. A student who misses more than one exam, he/she will have missed close to half the course material and may need to take the course again. Please contact Prof. Leininger to discuss such extreme situations.
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.
Viewing grades online:
You can always find the details of your worksheet, quiz, and exam
scores on Moodle. Course totals will be updated later in the semester. We will only use Moodle for grades unless otherwise
Details of your HW scores can be viewed on WebAssign, and will only be included into Moodle at the end of the semester.
Large-lecture Etiquette: Since there are over 100 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 to arrange special accommodations.
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: The TAs and I will hold office hours 4:00-5:00 pm, Monday, Tuesday, Wednesday, and Thursday in 347 Altgeld Hall. I will hold an additional office hour, 8:00-9:00 am Friday in my office, 366 Altgeld Hall. If those times don't work for you, and you cannot get the help you need on Piazza, you can make an appointment by sending Prof. Leininger an email or talking to him after class.
Piazza: Here you can find a discussion forum for this class. It is open only to students in 241H and will be moderated by the TAs who will typically check out the discussions once a day during the week.