Math 241 F1H
Midterm Exam 3 Review Sheet
General Information
- Special Open House: I will hold a special Open House a few
days before the exam, Monday, 11/26, 5 pm, in 241 Altgeld.
- Exam date, time, and location:
The exam will be given during the regular class time,
Wednesday, 11/28/2007, 2 - 2:50 pm, in the usual room, 142 Henry.
- Exam rules: The usual: No calculators, closed books/notes, no
formula sheets, and no cheating.
- Missed Exam policy. I don't give make-up exams, but
if you miss the exam with a valid
excuse (e.g., illness), the exam will be counted as "excused". (See the
Course Information Sheet for an
explanation of an "excused" exam score.)
The absence
must be documented by a letter from the Dean's Office at
300 Student Services Building, 610 East John St., phone 333-0050;
other documentation (e.g., note from McKinley) is not sufficient.
Exam content
The exam will cover Chapter 14 and Section 13.8, which was left-over
from Chapter 13.
I don't have past exams covering this material
(Chapter 14 was only recently added to the Calculus III syllabus
and this is the first time I'm teaching the new version of Calc III),
but the homework problems and the examples from in class and in the book
should give you a good idea of what to expect on the exam.
Here is a section-by-section syllabus of topics:
- 14.1:
Vector fields, curl, div, and grad
- 14.2: Line integrals, in various forms:
scalar/arclength
version, vector field/tangent version, explicit (coordinate) version.
Applications: work along path, mass and centroid of wire.
- 14.3:
Fundamental theorem for line integrals. Independence of path. Potential.
Conservative fields. Criterium/test for "conservative field in simply
connected region.
- 14.4:
Green's theorem (coordinate form and vector forms - see green handout).
Green's theorem area formula.
- 13.8:
Surfaces. Descriptions: as graph of z=f(x,y), and in parametric form
(via a function r(u,v)).
Surface area element (two formulas, one for surfaces z=f(x,y),
the other for parametrized surfaces), surface area.
- 14.5:
Surface integrals, in different forms: scalar
form, vector form (flux integral). Application: flux of a field through
a surface, mass and centroid of a surface
- 14.6:
The divergence theorem.
- 14.7:
Stokes's Theorem. Independence of path in 3 dimensions.
Conservative and irrotational fields. Potential.
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