M2E: FINAL EXAM INFORMATION
DATE OF THE EXAM: Monday, March 19, 2018
TIME: 8:00 -- 10:00 am
TOPICS COVERED: Sections 16.5 up to 16.9, included. The focus will be
on
(A) Green's theorem and its applications to curves in regions which are
connected but not simply connected (that is, the situations where there
is a ``hole" encircled by a closed curve). Sample Example:
Book, Section 16.4, Example 5 on p.1100
(B) Surface integrals of scalar functions over surfaces, with focus on
calculating mass and center of mass of objects in the shape of a
2-dimensional surface, given the density function.
Sample Example: Book, Section 16.7, Example 1 on p.1123 and
Example 3 on p.1125
(C) Surface integrals of vector field/flux of vector fields across oriented
surfaces. The focus will be on calculating the rate of flow of a fluid
across a given surface and the rate of heat flow.
Sample Example: Book, Section 16.7, Example 4 on p.1129, Example 5
on p.1130 and Example 6 on p.1132
(D) Applications of Stokes theorem in calculating the work done by a vector
field along a closed boundary of an oriented surface.
Sample Example: Book, Section 16.8, Example 1 on p.1136
(E) Applications of the Divergence theorem in calculating flux of a vector
field (flow of a fluid, heat flow) across the boundary of a simple solid
region in the 3-dimensional space. Sample Example: Book, Section
16.9, Examples 1 and 2 on p.1143
WRITING: Try to improve your writing from Midterm 2. You should include
all relevent information in your writing: Explain how you obtained your
integrated formula and bouds, and write down all steps which are relevant.
Study the examples in the book recommended in (A)-(E) above and look for what
information is relevant for the solutions, and how this information is written
up in the solutions. Try to get as close to this kind of writing as possible.
In order to give you all points you deserve, I need to see how you obtained the
relevant conclusions, so please show as much of your work as you can.
FORMAT OF THE EXAM: There will be five problems,
each worth 10 points. The level of difficulty will be the somewhat above that
in Midterm 2, which is due to more complex situations one encounters at higher
dimensions. On the other hand, you will have 2 hours for the exam.
EXAM RULES: Please refer to the general exam rules under ``Course
information and policies" on the course exam. In particular, no book, notes
and no electronic devices of any kind will be allowed.
GRADING: I will be grading the final exam, so please all questions
should be addressed to me (= the instructor). Otherwise, for general
information concerning grading, see again ``Course information and policies"
on the course website.
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MATH 2E
Last Modified: March 13, 2018