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 one
with 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.
Textbook
We will cover Chapters 12-16 of
James Stewart, Calculus: Early Transcendentals, 6th edition.
You will also need WebAssign
access to do the online homework. The U of I bookstore is selling a
bundle with both for $152, and the same is available from Cengage for
$131.00. If you already have the text from Calculus I or II here last
year, Cengage has agreed to provide WebAssign for free. Details of
this are being worked out, so for now, use WebAssign via the 14 day
free trial.
Course Policies
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: The in-class exams will be on September 22, October
20, and November 17 (all Wednesdays), and the final will be Friday,
December 10 from 8-11am. 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. A portion of this you will complete via
WebAssign, and will be due two
lectures later, just before 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.
Here's how to sign up for WebAssign and add yourself to my class. Go here and enter the Class Key:
uiuc 8585 1221
VERY IMPORTANT: When you create the account, it is crucial to
use your University of Illinois NetID as your account name. This is
crucial so that your HW scores will be credited toward your grade.
Technical issues with WebAssign should be addressed here.
Worksheets and Quizzes: Some section meetings will include 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 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 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 exam being returned.
Large-lecture Etiquette: Since there are 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 even 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.
Sources of help
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: Both myself and the section leaders
will hold regular office hours for you to ask questions about course
material, HW, etc.
Evening tutoring: The math department offers free evening
tutoring for this class, the details of which will be announced here. The same link
includes a list of private tutors for hire.
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
H. M. Schey, Div, Grad, Curl, and All That, W. W. Norton. A classic informal account of vector calculus from a physics point of view.
Aug 23. Introduction, Section 12.1. Notes.
WebAssign HW: None.
Other HW: Section 12.1: 1, 3, 5, 11, 25, 31.
Aug 25. Vectors (Section 12.2) and intro to the dot product (Section 12.3). Notes.
WebAssign HW: HW #1 (Due Monday, August 30)
Other HW: Section 12.2: 4, 5.
Aug 27. Applications of the dot product (Section 12.3) and equations for planes (Section 12.5). Notes.
WebAssign HW: HW #2 (Due Wed, Sept 1)
Other HW: Section 12.3: 1, 11, 53. Section 12.4: 43.
Oct 1. Introduction to space curves (Section 13.1, 13.2
(first half), 13.3) Notes. WebAssign HW: HW #14 (Due Wed,
Oct 6). Other HW: Section 13.1 #14, Section 13.2 #1, 4.
Oct 4. More on arc length (Section 13.3) and integrating
functions on curves (Section 16.2, pages 1034-1037) Notes. WebAssign HW: HW #15 (Due Fri,
Oct 8). Other HW: Section 13.3 #15.
Oct 6. Integrating functions on curves (Section 16.2, pages 1034-1037) Notes. WebAssign HW: HW #16 (Due Mon,
Oct 11). Other HW: Section 16.2: #37.
Oct 8. Vector fields (Section 16.1) and integrating them along curves (Section 16.2) Notes. WebAssign HW: HW #17 (Due Wed,
Oct 13). Other HW: Section 16.1 #35, Section 16.2 #17, 48.
Oct 11. More on integrating vector fields along curves (Sections 16.2 and 16.3) Notes. WebAssign HW: HW #18 (Due Fri,
Oct 15). Other HW: None
Oct 13. Conservative vector fields (Section 16.3) Notes. WebAssign HW: HW #19 (Due Mon, Oct 18). Other HW: Section 16.3: 11, 20, 23, 24, 26, 33.
Oct 15. Conservative vector fields II (Section 16.3) Notes.
WebAssign HW: Included with HW #19. Other HW: None. Last day to drop course.
Oct 18. Intro to multiple integrals (Section 15.1 and 15.2) Notes.
WebAssign HW: None.
Oct 22. Integrating over more complicated regions (Section 15.3 and 15.4) Notes.
WebAssign: HW #20 (Due Wednesday, Oct 27).
Other HW: Section 15.4 #1-4.
Oct 25. Polar coordinates (Section 15.4) and applications (Section 15.5).
Notes.
WebAssign: HW #21 (Due Friday, Oct 29).
Other HW: Section 15.4 #36.
Oct 27. Triple integrals (Section 15.6).
Notes.
WebAssign: HW #22 (Due Mon, Nov 1).
Other HW: Section 15.6 #27.
Oct 29. Integrating in cylindrical and spherical coordindates (Sections 15.7 and 15.8).
Notes.
WebAssign: HW #23 (Due Wed, Nov 3).
Other HW: Section 15.7 #29; Section 15.8 #7, 11, 28.
Nov 1. Changing coordinates I (Section 15.9).
Notes.
WebAssign: HW #24 (Due Fri, Nov 5).
Other HW: Section 15.9 #7, 9, 10.
Nov 3. Changing coordinates II (Section 15.9).
Notes.
WebAssign: HW #25 (Due Mon, Nov 8).
Other HW: Section 15.9: #17, 18, 24. Chapter 15 Review: #49.
Nov 5. Green's Theorem (Section 16.4).
Notes.
WebAssign: HW #26 (Due Wed, Nov 10).
Other HW: Section 16.4: #22, 27.
Nov 8. Surfaces in R^{3}(Section
16.6). Notes. WebAssign: HW #27 (Due
Fri, Nov 12). Other HW: None.
Nov 10. Area and integration on surfaces (Sections
16.6 and 16.7). Notes. WebAssign: HW #28 (Due
Mon, Nov 15). Other HW: Section 16.6 #60.
Nov 12. More on surface integrals (Section
16.7). Notes.
HW: included with previous assignment.
Nov 15. Divergence and applications (Section
16.5). (Not on exam) Notes.
HW: None.