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# chap2 - Chapter 2(partial Solutions Exercise 2.1(a X(x y...

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Chapter 2 (partial) Solutions Exercise 2.1 (a) X ( x, y ) = (0 , 1), a constant vector field. -10 -5 0 5 10 -10 -5 0 5 10 y x vector field: (x,y,0,1) The m-file below was used to generate the figure: % vector field: (x,y) ---> ((x,y),(0,1)) clear clf % pick grid large so arrows don’t overlap x=-10:2:10; [X Y]=meshgrid(x); % vector field U=zeros(size(X)); V=ones(size(X)); % plot field quiver(X,Y,U,V) % plot labels xlabel(’x’), ylabel(’y’) title(’vector field: (x,y,0,1)’) % print plot print -deps field1a.eps

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(b) X ( x, y ) = ( x, y ): -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 y x vector field: (x,y,-x,-y) The m-file: % vector field: (x,y) ---> ((x,y),-(x,y)) clear clf % choosing square grid x=-2:0.25:2; [X Y]=meshgrid(x); % vector field U=-X;V=-Y; % plot field quiver(X,Y,U,V) % plot labels xlabel(’x’), ylabel(’y’) % text(-0.9,0.25,’c=-1’) title(’vector field: (x,y,-x,-y)’) % print plot print -deps field1b.eps 2
(d) X ( x, y ) = ( y, x ): -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 y x vector field: (x,y,y,x) m-file: % vector field: (x,y)-->((x,y),(y,x)) clear clf % choosing square grid x=-2:0.25:2; [X Y]=meshgrid(x); % vector field U=Y;V=X; % plot field quiver(X,Y,U,V) % plot labels xlabel(’x’), ylabel(’y’) % text(-0.9,0.25,’c=-1’) title(’vector field: (x,y,y,x)’) % print plot print -deps field1d.eps 3

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Exercise 2.2 (a) f ( x, y ) = (1 , 1): -10 -5 0 5 10 -10 -5 0 5 10 y x
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