Unformatted text preview: F . At what points a does the mapping F have an inverse mapping in some neighbourhood of a ? b) Consider the region in the ±rst quadrant bounded by the lines xy = 0 , xy = 2 and the curves xy = 1 , xy = 4. Give a clearly labelled sketch of D xy in the xy – plane and of its image in the uv –plane. 5. a) Consider the transformation u = xy, v = 1 x + y . How is the area of a small bounded region in the xy –plane, A xy , containing the point (0 , 1) related to the area of its image in the uv –plane, A uv ? b) De±ne D xy = { ( x, y ) ∈ R 2 : 1 ≤ x + y ≤ 2 , y ≥ , x ≥ y } . Sketch D xy and its image under the transformation in (a). In both sketches provide the equations for the boundaries....
View
Full Document
 Spring '08
 WOLCZUK
 Math, Calculus, Linear Algebra, Derivative, Function composition, dxy, xy –plane

Click to edit the document details