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).


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Last update: January 23, 2014   11:39pm