Midterm2Review

# Midterm2Review - MATH 32B: MIDTERM 2 REVIEW PROBLEMS This...

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

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 ....
View Full Document

## 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.

Ask a homework question - tutors are online