Calculus in 3D
Department of Mathematical Sciences
CARNEGIE MELLON UNIVERSITY
21-259 Calulus in 3D, Spring 1999
Instructor: B. Doytchinov
Office: WeH6213
Office hours: Mo 10:00-11:30am, Fr 9:30-11:00am
e-mail:bd24@andrew.cmu.edu
COURSE CONTENTS
The course consists of four main parts:
- Vector Algebra and Vector-valued Functions. Coordinates
and vectors in 3D, dot product, cross product, equations of lines,
planes and quadric surfaces.
Parametric curves, arclength and curvature. Polar, cyllindrical and
spherical coordinates. Chapter 11, parts of Chapter 9.
- Functions of Several Variables. Limits, continuity,
differentiability, Chain Rule. Directional derivatives, gradient.
Minima and
maxima, Lagrange multipliers. Chapter 12.
- Multiple Integrals. Double and triple integrals. Change of
variable.
Chapter 13, parts of Chapter 9.
- Vector Calculus. Vector fields. Gradient, curl,
divergence. Green's
Theorem, Stokes' Theorem, the Divergence Theorem.
Chapter 14.
TEXT
J. Stewart. Calulus - Early Trancendentials, Third Edition,
Brooks/Cole 1995.
LECTURES and RECITATIONS
There are three lectures and two recitations per week. You are supposed
to attend all lectures and recitation. If you miss a class, it is your
responsibility to make a copy of the classnotes from another student
and make sure you learn what you have missed.
HOMEWORK
Homework is assigned each week, and is due on the Tuesday
of the following week. The homework will be collected in recitation, at
the beginning of the session. No late homework will be accepted.
Homework is a required component of the course. Working the
exercises will help you learn, and your graded homework will give you
some feedback on your progress. You are encouraged to discuss homework
problems with each other; however, the work handed in must be your own.
In particular, to avoid any perception of copying, you
should not read anybody else's work or show your work to anybody else.
GRADES
There will be four in-class tests and a Final exam. The lowest of the
four test scores will be dropped. The grade will be calculated in the
following way:
50% of the grade come from the three best Tests,
40% of the grade come from the Final Exam,
10% of the grade come from the 10 best homework scores.
Midsemester Grade
The midsemester grade will be calculated on the base of 60% of Test 1
and 40% of homework to date. No scores will be dropped in computing the
midsemester grade.
No makeup tests will be given - ever. If you miss a test,
that will be the one dropped when computing the semester score. Anybody
caught cheating on any of the tests or exams will be assigned a failing
grade for the course. Note that the finals session ends on May 11, so
you should plan on being in Pittsburgh until then.
FINAL EXAM
The final exam has been scheduled for Friday, May 07, 5:30-8:30pm.
The final exam will be comprehensive and will cover all the studied
material (up to and including the Divergence Theorem). Lagrange
Multipiers will not be on the final. In length
(number of problems) the test will be like two to two and a half tests.
The length of each problem will be approximately like on the tests. You
will be given all the formulas from the review sheets of all the tests,
plus the Divergence Theorem.
Calculus in 3D, Spring 1999
Send me mail:
bd24+@andrew.cmu.edu