MATH 2E WINTER 2014: FINAL EXAM
INFORMATION
Date/Time: Monday, March 17, 8:00am - 10:00am in DBH
1600
Format of the exam: The exam will contain six
problems, each covering one of the topics (a)-(f) below. Each
problem will be worth 5 points.
Topics: (a) Green's theorem: Applications to
calculate line integrals of vector fields along closed lines not
enclosing a singularity, and also enclosing a singularity.
(b) Determining whether a vector field in 3D is conservative,
and calculating the potential function.
(c) Surface integral of a function: Calculation of area of
the surface, mass and the center of gravity.
(d) Surface integral of a vector field: Calculation of flux
across a surface. Application to heat flow.
(e) Stokes theorem: Application in calculating a line
integral.
(f) Divergence theorem: Application in calculating the flux
across the boundary of a simple solid region.
Sample problems for the above listed topics: Coming
soon
For (a): Section 16.4 Exercise 9, 27
For (b): Section 16.5 Exercise 14, 16
For (c): Section 16.6 Exercise 44, 45; Section 16.7 Exercise 17, 39,
40
For (d): Section 16.7 Exercise 23, 27, 47
For (e): Section 16.8 Exercise 7-10, Section 16.10 Exercise 33
For (f): Section 16.9 Exercise 5, 7, 8, 11, 12; Section 16.10
Exercise 34
Recommendations:
1. Review calculations of single integrals. You will not be
required to evaluate complicated single integrals. However, most
single integrals that will appear in the problems on the final will
be very simple and no advanced integration techniques will be
needed. The focus will be on testing if you understand the new
material. If, in the course of computation you get a nasty integral,
this is a sign that you made a mistake -- go back and check your
work.
2. Review the material on linear and quadratic shapes:
2D: line, conic sections: circle, ellipse,
parabola, hyperbola.
3D: line, plane, sphere, cone, ellipsoid,
paraboloid, hyperboloid.
In particular, review the equations of these shapes and graphing the
shapes if the equation is given. Review the ways of parametrizing
such shapes. Also, review computation of the intersection of two
such shapes. Whenever you are working on a line/surface
integral, graph your surface, so that you have some idea and
intuition what is going on.
3. On the final you will be required to compute simple
integrals to the very end. Although the integrals on the midterm
will be simple, you will get some partial credit also when you set
up the main double or triple integral correctly, and make a mistake
in its evaluation. The amount of credit will depend on how far will
you get in the evaluation of the integral.
4. When evaluating multiple integrals, bear in mind that it
is essential to choose the right kind of coordinates (rectangular,
polar, cylindrical or spherical) and also the right order of
integration (review the type I, type II, and in 3D also type III
regions).
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Last update: March 12, 2014
11:05am