Honors | Honors Course in Calculus IV (MATH)
S312 | 7890 | Kevin Pilgrim


Math S312
Prof. K. Pilgrim
Spring 2005 Course Syllabus
Instructor: Kevin M. Pilgrim
Email: pilgrim@indiana.edu
Phone: 855-3477
WWW: http://mypage.iu.edu/ pilgrim
Office: 223 Rawles Hall
Hours: tba or by appointment
Course Meeting: tba

Catalog description: P: S311 or consent of department. Honors
version of M312. For students with unusual aptitude and motivation.
Credit not given for both M312 and S312. II Sem.

Texts: Flanigan and Kazdan, Calculus Two, 2nd ed. (Springer UTM);
Edwards, Advanced calculus of several variables (Dover).
About S311: Functions of several variables arise very naturally in
many applications. The simplest functions of several variables are
linear functions. So, we will first devote considerable time and
effort (about five weeks) to studying linear algebra, which is the
mechanics of dealing with linear functions. So, there will be a lot
of overlap with M/S 303. We will then define the concept of
derivative for a function of several variables using linear algebra.
Then we will begin our study of multivariable calculus in earnest.
There are a couple things you should know about this course:
• S311 is a first semester course of a two-semester sequence
S311/S312. We will study differentiation this term, integration next
term in S312. Students in M311 will study integration in several
variables; we will save this for next term.
• You will be expected to show a great deal of self-motivation and
independence. In particular, you will be expected to have read
carefully any assigned sections in the text so that you are prepared
for class meetings.
About S312: We will focus on integration in several variables. Our
approach will revolve around the notion of a “differential form”.
This is an elegant, unified way of doing integration over objects in
many dimensions. We will then derive the special formulas in
dimension three(div, grad, curl, and all that) which feature
prominently in M312. We will make extensive use of the linear
algebra vocabulary developed in S311.
Homework: Mathematics is not a spectator sport. The best way to
learn mathematics is to do it. Homework is an essential part of this
course and will be assigned and due weekly. There will be two
flavors of HW:
• Suggested problems: These are usually routine computations, often
with answers in the back of the book. You will be expected to master
the basic skills which go into these problems.
These may or may not be collected and briefly marked for grading.
• Graded problems: These are usually more involved problems. A
typical assignment will have a few problems where you are required
to supply “proofs”. We will talk about this process in our course.
Do not expect that you will be able to solve every graded problem!!
• Vocabulary: The writing and reading of math is not an imprecise
process. Understanding precisely definitions and statements of
theorems are crucial parts of a mathematicians’ training. Acquiring
new vocabulary will be almost a daily event and HW will reinforce
this.

Problem sessions: One meeting a week will be devoted to
a “recitation”. This will take the form of “problem sessions” where
you are to work in small groups on e.g. HW problems or problems
assigned by your TA. Attendance is mandatory and the expectation is
that you create a constructive environment for your peers.
Computer labs: On selected Mondays we will meet in Lindley Hall 025
during our normal class time to make use of the software package
Maple, which is useful for doing mathematics. I’ll show you the
basics but I will not provide other formal instruction–you will be
expected to get used to it on your own.
Citizenship: After a disappointing showing during an 8 AM course
last term I am forced to adopt the following policy. Attendance in
lecture, problem session, and computer lab is compulsory. You will
be required to sign in each day. More than one unexcused absence will
aect your grade. You are expected to: arrive promptly and prepared
for class; contribute to class discussion; contribute to a
constructive class environment by thinking of your classmates
as well as of yourself; make constructive use of oce hours and
problem sessions; ask questions when there are things you do not
understand.
Exams: There will be two in-class exams and one final exam.
Grading: Homework=40%; Midterms 2 @ 15% = 30 %; Final = 20%;
Citizenship 10%.
General: While written solutions to homeworks must be your own, you
are strongly encouraged to collaborate with your classmates. I
expect you to do the following:
• Read the assigned sections of the text before coming to class.
• Begin problem sets as soon as they are assigned. Often, this means
working on problems before we discuss the section in class.
• The general rule of thumb: you spend 3 hours outside of class for
every one hour in class.
This is a four-credit-hour honors class, so this translates into 12
hours of out-of-class work per week, minimum. (It took me 40 hours
of study to get the basics of electron orbitals way back in ’85...)
• Ask lots of questions. The more specific you can make them, the
better I can answer them.
• Visit me during my oce hours, or come see me to arrange a
mutually convenient time.
Note: you are now enrolled in an honors upper-division mathematics
course at a world-class research university. Act accordingly.
Success in this class will largely depend on the effort you spend
outside of class.