Mathematics 2411 Honors Calculus III Course
Description
Spring, 2013
(TTh 3:05 in the
Clough Undergraduate Learning Commons, room 102, with recitations MW in
Skiles 270
)
Instructor: Evans Harrell, Office Skiles 218D, 894 3300,
harrell at math.gatech.edu
Instructor's office periods: Monday 11:00-12:00 and Thursday 11:30-12:30
at Skiles 218D. Ordinarily I will
also be available for 20 minutes after each class.
Recitation:
Class web page
The class will be coordinated through
T-Square, but you can also consult the
Class web page
directly.
It
is your responsibility to consult
T-Square
or the web page regularly for information
about the class,
such as homework assignments. You will also be in
e-mail contact with the instructor and the teaching assistant, and we will do
our best to respond to your questions.
Required texts and materials
We will use Marsden and Tromba, Vector Calculus, and on-line materials, which
may be linked to from the class website or T-Square. You are also required to have a clicker
for classroom use.
Description: Calculus is not only essential in engineering; it is
one of mankind's greatest intellectual achievements. After thousands of years
of confusion on the part of philosophers, Newton, Leibniz, and Euler created
effective conceptual tools for understanding the infinite and the infinitesimal. In the third
term of calculus we learn about derivatives and integrals in
three (or even more) dimensions and their uses.
Grading and requirements
There will be
tests in the recitations on
- Wednesday, 23 January,
- Wednesday, 13 February,
- Wednesday, 13 March,
- Wednesday, 10 April,
There will also be a final exam, of course. Homework will be collected on
Tuesdays, and there will be regular clicker quizzes. Your homework-quiz
average will incorporate at least two drops. In addition, Prof. Harrell
may announce occasional contests, and the winner of a contest will
receive a small number of extra-credit points.
Students' grades will depend on the following quantity:
(T1 + T2 + T3 + T4 + HQ + F - min(T1..T4,F) ) + E + F/2
where the components of this formula correspond to the ingredients
mentioned above, after scaling so that all of them except E = extra credit
total have a common median of 70. The drop
in the formula is the mechanism for coping with personal events
such as illness and family emergencies.
There will be no opportunities for
make-up tests after the fact. In the event of an absence due
to travel representing Georgia Tech, such as an intercollegiate sports
competition, you must
notify the professor at least two weeks in advance to
arrange an early test or other alternative. Otherwise, such
absences will be treated as personal.
Calculators and tests
No restrictions will be placed on the use of
calculators that do elementary mathematics on the tests.
Calculators that can do calculus symbolically shall not be brought to
tests. No credit will be given on tests for a correct answer without the
intermediate steps.
Readings
The schedule of reading will be posted on the
2411 assignments page and on T-Square.
The subject matter covered will be roughly the following:
Parametrized paths, velocity and acceleration, curvature and arclength
Continuity, etc. for functions of several variables. Graphs and contour plots
Partial derivatives and the chain rule. Taylor's theorem in several variables
The gradient, tangent planes, best linear approximation and best quadratic approximation
Optimization, types of critical points
Lagrange multipliers, Newton's method in several variables
Double integrals, iterated integrals. Applications: area, center of mass, and volume by Pappus's Theorem
Area integrals in polar coordinates, general coordinates and the Jacobian in the plane
Triple integrals, spherical and cylindrical coordinates
Jacobian in three variables. Improper multiple integrals and applications
Vector fields and line integrals, work and flux
Green's theorem in the plane for both work and flux integrals. Exact vector fields
Parameterized surfaces and surface integrals
Gauss's Theorem and Stokes's Theorem
Applications
On-line materials
This course will benefit from occasional on-line materials, which may require
the software in the student software suite, especially Netscape, Maple,
and Acrobat. There is a home page for the class at
http://www.math.gatech.edu/~harrell/2411S13/.
Scientists and Engineers today do mathematics differently than in the
past. Complicated
calculations can be done with software such as Maple,
Mathematica, or Matlab, and there are many
powerful items on the World Wide Web to help you both to learn mathematics and
to do it effectively.
We hope that you will use software and
the Internet to help with calculations and learning, but
always remember that real understanding requires you to exercise
your mind as well as your fingers.
Learning Disabilities
It is the right of any student with a certified learning disability to request necessary accommodation. Such requests must be made well in advance of the time that the accommodation is required and a letter of documentation from the
ADAPTS office
must be presented at the time of any request.
Academic Honesty
It is expected that all students are aware of their individual responsibilities under the
Georgia Tech Academic Honor Code, which will be strictly adhered to in this class.
THIS PAGE IS NOT A PUBLICATION OF THE GEORGIA
INSTITUTE OF TECHNOLOGY AND THE GEORGIA INSTITUTE
OF TECHNOLOGY HAS NOT EDITED OR EXAMINED
THE CONTENT. THE AUTHOR(S) OF THE PAGE ARE SOLELY
RESPONSIBLE FOR THE CONTENT.
Return to the
2411 class web page