CALCULUS III
1. General Information
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Course: Math 226 (Calculus III), Fall 2012 (section 39563R)
Prerequisites: MATH 126
Time: MWF 11:00-11:50am
Location: GFS 116
Instructor: Sabin Cautis, KAP 400C, cautis@usc.edu
Office Hours: Monday and Wednesday 1:30-2:30pm or after class
Course website: includes syllabus and homework assignments
http://www-bcf.usc.edu/∼cautis/calcIII/
Only homework and exam grades will be posted on Blackboard.
• Text: Essential Calculus by James Stewart
• TA: Tsilifis, Panagiotis, tsilifis@usc.edu
• Discussion session: TTh 11am-1pm VHE 214
Homework: Homework will be assigned on Wednesdays and due the following Wednesday. They
will be collected at the end of class without exception (no late homework accepted but the lowest
grade is dropped). Assignments, with their due date, are available on the course website.
You may get help from any source but you are strongly encouraged to attempt the problems yourself
before seeking assistance. Any written work submitted must be your own. Your submitted work must
be stapled together and should have your name on every page. Unstapled pages with no name will
be discarded.
Tests: There will be two midterm exams and a final exam. The tests will be closed book-closed
notes tests. Calculators will not be allowed. The (tentative) dates for the two midterms will be:
Wednesday October 3rd and Wednesday November 14th.
Final Exam: The final exam is currently projected for Monday, December 17, 4:30–6:30 p.m.
Book your travels accordingly!
Grades: Grades will be computed as follows: Homework: 20 % (the lowest homework score will
be dropped), Midterms 25% each, Final 30%.
Synopsis: The course will cover chapters 10-13 of the book.
The usual fundamental theorem of calculus (which we all should be very familiar with by now) is
df
over a region (in this case the region is an interval) and the
a relationship between the integral of dx
integral of f over the boundary of the region (which in this case is two endpoints and this amounts to
evaluating f at these two points).
This theorem has analogues in every dimension. In dimensions 3 these go by the name of the
divergence and Stokes’ theorem. They are quite fundamental and have important applications. For
example, basic results in electrodynamics are essentially applications of these theorems. The aim of
this course is to get to the point of understanding the statements and contents of these theorems and
how to apply them.
We begin by discussing a fundamental tool, namely vectors in 2 and 3 dimensions (chapter 10).
Using them one can generalize the idea of derivatives and integrals from 1 to 2 and 3 dimensions
(chapters 11,12). Finally, we discuss theorems like the divergence and Stokes’ theorem (chapter 13).
Help Rooms: The Math Center is located in KAP 263 and is open from 8am until at least 5pm
Monday through Thursday and from 8am to 4pm on Friday. Your TA will have office hours in the
Math Center, but you are free to use the Math Center at any time.
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CALCULUS III
Supplemental instruction The are weekly study sessions held by a Supplemental Instruction
Leader. See http://dornsife.usc.edu/math226/ for more information.
Other Advice Unlike a novel, reading mathematics is a slow process. One could very well spend
hours reading one page. So read it carefully until you understand. Be patient!
Getting help. If you’re having trouble, get help immediately. Everyone who works seriously on
mathematics struggles. But if you don’t get help promptly you will soon be completely lost. The
first places to look for help are my office hours, the course TA in the help room and the SI sessions.
Talking to your other classmates can also be very helpful.
Teach to learn! The best way to learn mathematics is to explain it to someone. You’ll find that,
particularly in office hours, I’ll try to get you to explain the ideas. You should also try explaining the
material to each other. The person doing the explaining will generally learn more than the explainee.
Students with disabilities Any student requesting academic accommodations based on a disability is required to register with Disability Services and Programs (DSP) each semester. A letter
of verification for approved accommodations can be obtained from DSP. Please deliver this letter to
me as early in the semester as possible. DSP is located in STU 301 and is open 8:30 am - 5:00 pm,
Monday through Friday.
2. Schedule
Very rough course schedule, subject to later adjustments:
• Aug 27/29/31 sect. 10.1-10.3:
Overview. Coordinate systems, vectors and dot products.
• Sep 5/7 sect. 10.4-10.5:
Cross product, equations for lines and planes (parametric, implicit)
• Sep 10/12/14 sect. 10.6-10.7:
Cylinders and other surfaces. Vector valued functions and space curves.
• Sep 17/19/21 sect. 10.8, 11.1-11.2:
Arc length. Functions of several variables. Limits and continuity.
• Sep 24/26/28 sect. 11.3-11.4:
Partial derivatives. Tangent planes and linear approximation.
• Oct 1 sect. Review.
• Oct 3 Midterm #1 (sections 10.1-11.2)
• Oct 5 sect. 11.5:
The chain rule, implicit differentiation.
• Oct 8/10/12 sect. 11.6-11.7:
Directional derivatives and the gradient. Max/min problems.
• Oct 15/17/19 sect. 11.8, 12.1:
Lagrange multipliers. Double integrals.
• Oct 22/24/26 sect. 12.2-12.4:
More general double integrals (like in polar coordinates) and applications.
• Oct-Nov 29/31/1 sect. 12.5-12.7 :
Triple integrals in rectangular, cylindrical and spherical coordinates.
• Nov 5/7/9 sect. 12.8, 13.1-13.2 :
Change of variables. Vector fields and line integrals.
• Nov 12 Review.
• Nov 14 Midterm #2 (sections 11.3-12.8)
• Nov 16 sect. 13.3:
Fundamental theorem of line integrals.
• Nov 19/21 sect. 13.4:
Green’s theorem.
• Nov 26/28/30 sect. 13.5-13.6:
Curl and divergence. Parametrized surfaces and surface area.
• Dec 3/5/7 sect. 13.7-13.8 + Review.
Surface integrals and Stokes’ theorem.