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Test_2_description - and 13.2 4 Double integrals over...

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MATH 251, Section 502, Test #2, Fall 2010 Friday, October 29, Blocker 166, 6:00 – 8:00 pm Calculators are OK, but not necessary. There will be 10 problems of equal weight 10 pts for a maximal score 100 pts. For full credit you need to show the whole work. The problems are aimed to test your knowledge (definitions and main results), understanding of the material (main mathematical ideas and techniques) and some basic applications. The test is based on your homework assignments and covers Sections 12.7 – 12.8 of Chapter 12 and Sections 13.1 – 13.3, 13.5, 13.8 - 13.10 of Chapter 13 and also on the Review problems of Chepters 12 and 13 that are related to these sections. 1. Absolute minimum and maximum of functions of 2 and 3 variable. This is the second part of Section 12.7. 2. Method of Lagrange multipliers for minimizing or maximizing a function subject to constrains. The Section 12.8 is a must . 3. Double integrals over rectangle, iterated integrals, Fubini’s theorem. (Sections 13.1
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Unformatted text preview: and 13.2). 4. Double integrals over general regions. Most important: you should be able to describe the domain in a fashion that is useful for evaluating the integral. Also, you should be able to sketch the domain or to change the order of integration. 5. Double integrals in polar coordinates, Sections 13.5. Most important: you should be able to work with curves in polar coordinates and to describe domains in polar coordinates and evaluate integral in polar coordinates. 6. From Section 13.6 you need to know about how to compute the mass, the rest of the material is not included. 7. Triple integrals over general domains. Most important: you should be able to describe a domain bounded by various surfaces (planes, cylinders, spheres, etc) in a convenient for the integration way. This is Section 13.8. 8. Cylindrical and spherical coordinates, Section 13.9. 9. Triple integrals in cylindrical and spherical coordinates, Section 13.10. 10. Good luck...
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