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# You must use the display command dened in the plots

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Unformatted text preview: Inequalities • Plots with logarithmic scales • Density functions • Contours as in a topographical map • Conformal plots of complex functions • Vector ﬁelds • Curves in three-dimensional space • Objects of type Matrix • Root loci • Vectors in two and three-dimensional space • Plots in the visualization component of the Student package For further explanation of a particular plot command, refer to ?plots,command . > with(plots): Plot implicitly deﬁned functions by using implicitplot. > implicitplot( x^2+y^2=1, x=-1..1, y=-1..1, scaling= > constrained ); 1 y 0.5 –1 –0.5 0 0.5 x 1 –0.5 –1 5.6 Special Types of Plots • 139 The following is a plot of the region satisfying the inequalities x + y < 5, 0 < x, and x ≤ 4. > inequal( {x+y<5, 0<x, x<=4}, x=-1..5, y=-10..10, > optionsexcluded=(color=yellow) ); 10 5 –1 –5 –10 1 2 3 4 5 Here the vertical axis has a logarithmic scale. > logplot( 10^x, x=0..10 ); 1e+10 1e+09 1e+08 1e+07 1e+06 1e+05 .1e5 .1e4 .1e3 .1e2 1. 2 4 x 6 8 10 A semilogplot has a logarithmic horizontal axis. > semilogplot( 2^(sin(x)), x=1..10 ); 2 1.8 1.6 1.4 1.2 1 0.8 0.6 1. 2. x 4. 7. .1e2 140 • Chapter 5: Plotting Maple can also create plots where both axes have logarithmic scales. > loglogplot( x^17, x=1..7 ); 1e+14 1e+13 1e+12 1e+11 1e+10 1e+09 1e+08 1e+07 1e+06 1e+05 .1e5 .1e4 .1e3 .1e2 1. 2. x 4. 7. In a densityplot, lighter shading indicates a larger function value. > densityplot( sin(x*y), x=-1..1, y=-1..1 ); 1 y 0.5 –1 –0.5 –0.5 –1 0.5 x 1 Along the following curves, sin(xy ) is constant, as in a topographical map. > contourplot(sin(x*y),x=-10..10,y=-10..10); 10 y 5 –10 –5 0 –5 –10 5 x 10 5.6 Special Types of Plots • 141 A rectangular grid in the complex plane becomes the following graph when you map it by z → z 2 . > conformal( z^2, z=0..2+2*I ); 8 6 4 2 –4 –2 0 2 4 The fieldplot command draws the given vector for many values of x and y. That is, it plots a vector ﬁeld, such as a magnetic ﬁeld. > fieldplot( [y*cos(x*y), x*cos(x*y)], x=-1..1, y=-1..1); 1 y 0.5 –1 –0.5 –0.5 –1 0.5 x 1 Maple can draw curves in three-dimensional space. > spacecurve( [cos(t),sin(t),t], t=0..12 ); 142 • Chapter 5: Plotting Here Maple inﬂates the previous spacecurve to form a tube. > tubeplot( [cos(t),sin(t),t], t=0..4*Pi, radius=0.5 ); The matrixplot command plots the values of a object of type Matrix. > A := LinearAlgebra[HilbertMatrix](8): > B := LinearAlgebra[ToeplitzMatrix]([1,2,3,4,-4,-3,-2,-1], > symmetric): > matrixplot( A+B, heights=histogram, axes=frame, > gap=0.25, style=patch); 4 2 0 –2 –4 2 4 column 6 8 8 6 4 row 2 The following is a demonstration of a root locus plot. > rootlocus( (s^5-1)/(s^2+1), s, -5..5, style=point, > adaptive=false ); 5.6 Special Types of Plots • 143 1 0.5 0 –0.5 –1 –1.5 –1 –0.5 0 0.5 1 1.5 The arrow command plots arrows or vectors in two or three dimensions. > plots...
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