· PROFESSOR:
Arkady Berenstein, 306
Fenton Hall, Phone: 346-5624, Email: arkadiy@uoregon.edu
·
CLASSES: 360 Condon Hall, TR, 16:00--17:50
·
OFFICE HOURS: W
15:00—16:30 (or by appointment, please use email).
·
TEXT:
James Stewart, (MultiVariable) Calculus, 8th Edition,
Cengage Learning, 2015,
·
PREREQUISITES: Math 281.
·
COURSE CONTENT:
This is the second term of the multivariable calculus sequence. The course
covers two big topics. The first topic is double and triple integrals with
applications to volumes of solids. The second topic is the 3D differential
geometry including vector fields and surface integration with an emphasis on
Green's Theorem, Stokes' Theorem and Divergence Theorem. Specific learning outcomes include:
· evaluation of integrals
over regions in the plane and in space both as iterated integrals and by
applying the change of variable theorem.
· using spherical, cylindrical, polar elliptical and toroidal
coordinates and common transformations in these calculations.
· computing the center of mass and the total mass of a region with a variable mass
density
· computing certain improper integrals, surface are integrals, arc length
integrals, line integrals, and flux integrals.
· finding the work done and the mass flow across a
membrane as well as center of gravity and total mass of a thin wire or a
membrane
· computing the gradient, curl, and divergence of vector fields
· determining if a vector field is conservative and, if so, finding the potential
function
· evaluating certain line integrals
· understanding both sides of the equations and the hypotheses in Green's, Stokes', and
Gauss's theorems
· using these 3 results to push curves around and surfaces around to evaluate
flux and line integrals of certain vector fields
· using Green's theorem to evaluate certain area integrals in the plane and
find their centers of mass
·
ATTENDANCE: Please remember that if you miss a class it is your responsibility to
find out what happened in that class.
·
COURSE WEB PAGE:
The homework and other class material are also available at the web page http://pages.uoregon.edu/arkadiy/282new.html
·
GRADING: Total 100%. Will be based on:
·
HOMEWORK (20%): Homework due on Thursdays. The first homework is due on
Thursday April 11. Late homework will not be accepted. I will choose a
subset of the assigned problems to be graded. The lowest homework score will be
dropped.
·
QUIZZES (10%) There will be short quizzes on Thursdays Week 2, 4, 7, and 9.
They will be based on the material covered in the previous week's homework.
·
MIDTERM 1 (20%) on Thursday May 2.
· MIDTERM
2 (20%) on Thursday May 23.
· FINAL
(30%) on Monday June 10, 12-30-14:30.
·
REMARK. You may bring a 3x5 inch index card with any formulas on it to any
exam or quiz if you wish. You may use a handheld graphing calculator to any
exam or quiz.
Tentative Schedule
|
Week 1/Apr. 1-5 |
sections 15.1, 15.2, 15.3 |
|
Week 2/Apr. 8-12 |
sections 15.3, 15.4, 15.5, Quiz 1 |
|
Week 3/Apr. 15-19 |
sections 15.5, 15.6, 15.7 |
|
Week 4/Apr. 22-26** |
sections 15.7, 15.8, 15.9, Quiz 2 |
|
Week 5/Apr. 29-May 3** |
sections 15.9, 16.1, Review, Midterm 1 |
|
Week 6/May 6-10 |
sections 16.2, 16.3, 16.4 |
|
Week 7/May 13-17 |
sections 16.4, 16.5, Quiz 3 |
|
Week 8/May 20-24 |
sections 16.6, Review, Midterm 2 |
|
Week 9/May 27*-31 |
sections 16.7, 16.8, 16.9, Quiz 4 |
|
Week 10/Jun. 3-7 |
section 16.9, Review |
*No class on May 27 - Memorial Day
holiday
**I will not be around on Tuesday of Week 4 and Tuesday of Week 5. The classes
will be covered via zoom or by other professors.
Important dates (See Schedule of Courses or Academic
Calendar):
Mar 31:
Last day to drop a class without a "W;"
Apr 8: Last day to add a
class;
May 19: Last day to drop a class with a "W", change grade options
(Graded or P/N).