MATH 2E MIDTERM 2 INFORMATION

Date: Wednesday, February 19, 2014 

Topics: (a) Change of coordinates in multiple integrals
(b) Line integral of a function with respect to the arc length, and applications: Computation of length of a curve, mass from a given linear density, moments, and center of gravity.
(c) Line integral of a vector field and application: Computation of the work done by the vector field when seen as a force field.
(d) Fundamental theorem for line integrals: Determining whether a given vector field is conservative and computation of the potential function.

Sample problems: 
Section 15.10: 23, 24, 25
Section 16.2: 7, 11, 15, 21, 33, 36, 40, 41
Section 16.3: 7, 13, 15, 17, 23, 24

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).

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Last update: February 12, 2014   6:57pm