Calc3_RV3

Calc3_RV3 - MAC 2311 Calculus III UNIV. REVIEW FOR TEST #3...

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MAC 2311 – Calculus III FLORIDA INTERNATIONAL UNIV. REVIEW FOR TEST #3 FALL 2011 REMEMBER TO BRING AN 8x11 BLUE EXAM BOOKLET FOR THE TEST Relevant sections of the textbook : [Ch.14: Sec 14.5-14.8 and Ch.15: Sec. 15.1-15.8.] MAIN PROBLEM SOLVING TECHNIQUES : 1. How to find the volume of solid regions by using triple integrals . 2. How to find triple integrals by using cylindrical coordinates and spherical coordinates . 3. How to find the Jacobian and how to use it to change an integral w.r.t. to one set of variables into an integral w.r.t. another set of variables. 4. How to find the mass and center of gravity of a lamina (or, of a solid body) with a given density by using double integrals (or triple integrals, respectively). 5. How to find the mass and center of gravity of a curved wire (or, of a curved surface) with a given density by using a line integral (or a surface integral , respectively) in a scalar field . 6. How to use the centroid of a curve (or, of a lamina) and Pappus’ Theorem to find the surface area of a surface of revolution (or the volume of a solid of revolution, respectively). 7. How to make a sketch of a vector field and how to find the gradient , divergence , curl and Laplacian of the vector field. 8. How to find the work done by a vector field on a particle by using a line integral in a vector field . 9.
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Calc3_RV3 - MAC 2311 Calculus III UNIV. REVIEW FOR TEST #3...

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