If your solution to stated problem does not match the given solution, you should self-critique per instructions at

   http://vhcc2.vhcc.edu/dsmith/geninfo/labrynth_created_fall_05/levl1_22/levl2_81/file3_259.htm

.

Your solution, attempt at solution.  If you are unable to attempt a solution, give a phrase-by-phrase interpretation of the problem along with a statement of what you do or do not understand about it.  This response should be given, based on the work you did in completing the assignment, before you look at the given solution.

At the end of this document, after the qa problems (which provide you with questions and solutions), there is a series of Questions, Problems and Exercises. 

Question:  `q001.  Find the Jacobian d(x,y,z)/d(u,v,w)  when x = 2u - v, y = 2v + 2w, z = v - w.

Your solution: 

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Given Solution: 

Self-critique (if necessary):

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Question:  `q002.  Let R be the parallelogram with vertices (0,0), (1,4), (4,6), (4,2). Sketch and decribe the corresponding region after the transformation u = x^2, v = x+ y.

Your solution: 

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Given Solution: 

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Question:  `q003.  Under the transformation u = 1/5(2x + y) and v = 1/5(x - 2y) the region D which is a square in the xy-plane with vertices (0,0), (1,-2) is mapped onto a square in the uv-plane. Use this information to find the integral of cos(2x + y)*sin(x - 2y) with respect to V over D.

Your solution: 

Confidence rating:
 

Given Solution: 

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Question:  `q004.  A rotation of the xy-plane through the fixed angle theta is given by x = u cos(theta) - v sin(theta), y = u sin(theta) + v cos(theta).

• Compute the Jacobian of this transformation.
• Let E denote the ellipse x^2 + xy + y^2 = 9. Use a rotation of pi/4 to obtain an integral which is equivalent to the double integral of y with respect to V over E.
• Evaluate the integral found in the previous step.

Your solution: 

Confidence rating:
 

Given Solution: 

Self-critique (if necessary):

Self-critique rating: