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Gradient & Mathematical Modeling and Simulation Using MATLAB Prof. Muhammad Saeed
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Gradient I: x =-2:0.2:2; y = x.* exp(-x.^2); px = gradient(y,.2); quiver(x,px)
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Gradient II: [x,y] = meshgrid(-2:0.2:2); z = x.* exp(-x.^2 - y.^2); [px,py] = gradient(z,.2,.2); contour(x,y,z), hold on, quiver(x,y,px,py), hold off
![Gradient II: [x,y] = meshgrid(-2:0.2:2); z = x.* exp(-x.^2 - y.^2); [px,py] = gradient(z,.2,.2); contour(x,y,z), hold on, quiver(x,y,px,py), hold off](http://images.slideplayer.com/2/718103/slides/slide_3.jpg "Gradient II: [x,y] = meshgrid(-2:0.2:2); z = x.* exp(-x.^2 - y.^2); [px,py] = gradient(z,.2,.2); contour(x,y,z), hold on, quiver(x,y,px,py), hold off")
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Gradient II: [x,y] = meshgrid(-2:0.2:2); u = x.* exp(-x.^2 - y.^2); [gx,gy] = gradient(u,.2,.2); contour(x,y,u), hold on, quiver(x,y,gx,gy), hold off
![Gradient II: [x,y] = meshgrid(-2:0.2:2); u = x.* exp(-x.^2 - y.^2); [gx,gy] = gradient(u,.2,.2); contour(x,y,u), hold on, quiver(x,y,gx,gy), hold off](http://images.slideplayer.com/2/718103/slides/slide_4.jpg "Gradient II: [x,y] = meshgrid(-2:0.2:2); u = x.* exp(-x.^2 - y.^2); [gx,gy] = gradient(u,.2,.2); contour(x,y,u), hold on, quiver(x,y,gx,gy), hold off")
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[x,y] = meshgrid(-4:4,-3:3); u = x.*x+y.*y; v = 4*del2(u) V = 4 4 4 4 4 4 4 4 4
![[x,y] = meshgrid(-4:4,-3:3); u = x.*x+y.*y; v = 4*del2(u) V =](http://images.slideplayer.com/2/718103/slides/slide_5.jpg "[x,y] = meshgrid(-4:4,-3:3); u = x.*x+y.*y; v = 4*del2(u) V =")
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[x,y,z] = meshgrid(-3:3,-3:3,-3:3); u = x.*x + y.*y + z.*z; v = 6*del2(u)
![[x,y,z] = meshgrid(-3:3,-3:3,-3:3); u = x.*x + y.*y + z.*z; v = 6*del2(u)](http://images.slideplayer.com/2/718103/slides/slide_6.jpg "[x,y,z] = meshgrid(-3:3,-3:3,-3:3); u = x.*x + y.*y + z.*z; v = 6*del2(u)")
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v(:,:,1) = 6 6 6 6 6 6 6 v(:,:,2) = 6 6 6 6 6 6 6 v(:,:,3) = 6 6 6 6 6 6 6 v(:,:,4) = 6 6 6 6 6 6 6 v(:,:,5) = 6 6 6 6 6 6 6 v(:,:,6) = 6 6 6 6 6 6 6 v(:,:,7) = 6 6 6 6 6 6 6
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