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# Test_3_description - 3 Line integrals of vector ﬁelds(end...

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MATH 251 section 502, Content of TEST #3, Fall 2010 Calculators are OK, but not necessary. There will be 10 problems of equal weight 5 pts for a maximal score 50 pts. For full credit you need to show the whole work. The problems are aimed to test your knowledge (definitions, the main theorems), under- standing of the material (main mathematical ideas and techniques) and some basic applica- tions. The test will be based on the basic material of your textbook and your homework assign- ments, it will cover the Section 14.1 - 14.9. You should be able to state important theorems like Fundamental Theorem for Line Integrals, Green’s Theorem, Stokes’ Theorem, and Di- vergence Theorem (do not forget the “fine print” !!!). The problems will cover the following material: 1. Vector fields in 3-D, conservative vector fields. 2. Line integrals of functions (of two and three variables) and application to mass.
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Unformatted text preview: 3. Line integrals of vector ﬁelds (end of section 14.2) and applications. 4. Line integrals of conservative vector ﬁelds, independence of the path. Criterion for a vector ﬁeld to be conservative. Fundamental Theorem for line integrals. All these are must (in particular ﬁnding a potential of a given conservative vector ﬁeld). 5. Green’s Theorem and applications (this is an absolute must ). 6. Diﬀerential operators over vector ﬁelds, curl , grad , and div , and their properties. 7. Parametric surfaces and their area. 8. Surface integrals of scalar functions. Surface integrals of vector ﬁelds ( a must !) 9. Surface integrals of vector ﬁelds and application (an absolute must ). 10. Stokes’ Theorem and applications a must . 11. The Divergence Theorem (section 14.9) 12. Good luck...
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