MATH 2E MIDTERM 1 INFORMATION
Date: Monday, January 27, 2014
Topics: (a) Double and triple integrals and their
evaluations in rectangular, polar, cylindrical and spherical
coordinates.
(b) Application: Calculating mass from density.
Sample problems:
Section 15.3: 16
Section 15.4: 25
Section 15.5: 3 Only the part on mass.
Section 15.7: 17
Section 15.8: 19
Section 15.9: 25
Format of the exam: There will be four problems, each
worth 5 points.
Recommendations:
1. Review calculations of single integrals. However, all
integrals on the midterm 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. Also, review computation of the
intersection of two such shapes.
3. On the midterm you will be required to compute the
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).
HOME
MATH 2E
Last update: January 23, 2014
11:39pm