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Problems and solutions Session 5

Problems and solutions Session 5. Problems. Draw the contour plot of function F(x,y) = x 1.5 y 2 exp(-(x-2)-(y-0.5)) on [0,5]x[0,5] and its gradient field with quiver command in the same picture. Use meshgrid to create the X,Y –grid.

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Problems and solutions Session 5

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  1. Problems and solutionsSession 5

  2. Problems • Draw the contour plot of function F(x,y) = x1.5y2exp(-(x-2)-(y-0.5)) on [0,5]x[0,5] and its gradient field with quiver command in the same picture. • Use meshgrid to create the X,Y –grid. • Compute the derivative by hand or by using your earlier differf.m function. • Make a histogram of points randn(10000,1). Introduction to MATLAB - Solutions 5

  3. x = 0:.25:5; % negative x gives complex values, so change the domain [X,Y] = meshgrid(x,x); expterm = @(X,Y) exp(-(X-2)-(Y-0.5)); FXY = X.^1.5.*Y.^2.*expterm(X,Y); dxFXY = 1.5*sqrt(X).*Y.^2.*expterm(X,Y)- FXY; dyFXY = 2*X.^1.5.*Y.*expterm(X,Y)-FXY; contour(X,Y,FXY) hold on quiver(X,Y,dxFXY,dyFXY) hold off hist(randn(10000,1),50) Some solutions Introduction to MATLAB - Solutions 5

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