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Unformatted text preview: MATH 32B: MIDTERM 2 REVIEW PROBLEMS This midterm covers sections 16.9-17.4 of the textbook. There are two major topics in these sections: the change of variables for multiple integrals and line integrals. Problem 1. Evaluate RR R e x + y dA where R is the region given by the inequality | x | + | y | 1 using a proper change of variables. Problem 2. Write down the transformations that give rise to polar, cylindrical, and spherical coordinates and find the Jacobian of each transformation. Problem 3. Evaluate RR R sin(9 x 2 + 4 y 2 ) dA where R is the region bounded by the ellipse 9 x 2 + 4 y 2 = 1. Problem 4. Find the Jacobian of the transformation x = e u + v , y = e u- v , z = e u + v + w . Problem 5. Use a proper change of coordinates to find the area of the ellipse x 2 /a 2 + y 2 /b 2 = 1 and the volume of the ellipsoid x 2 /a 2 + y 2 /b 2 + z 2 /c 2 = 1. Problem 6. Find the gradient of the functions f ( x,y,z ) = e xy z and g ( x,y ) = x 2 y 2 + sin( x )cos( y ) i ....
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This note was uploaded on 06/03/2011 for the course PHYSICS 1B 1b taught by Professor Corbin during the Winter '10 term at UCLA.
- Winter '10