Unformatted text preview: following plot is unconstrained.
> plot( exp(x), x=0..3 );
20 18 16 14 12 10 8 6 4 2 0 0.5 1 1.5 x 2 2.5 3 The following is the constrained version of the same plot.
> plot( exp(x), x=0..3, scaling=constrained); 108 • Chapter 5: Plotting 20 18 16 14 12 10 8 6 4 2 012 3 x Polar Coordinates
Cartesian (ordinary) coordinates is the Maple default and is one among many ways of specifying a point in the plane. Polar coordinates, (r, θ), can also be used. In polar coordinates, r is the distance from the origin to the point, while θ is the angle, measured in the counterclockwise direction, between the xaxis and the line through the origin and the point. You can plot a function in polar coordinates by using the polarplot command in the plots package. To access the short form of this command, you must ﬁrst employ the with(plots) command.
> with(plots): Figure 4.1 The Polar Coordinate System r y θ
0 x Use the following syntax to plot graphs in polar coordinates. 5.1 Graphing in Two Dimensions • 109 polarplot( rexpr, angle =range ) In polar coordinates, you can specify the circle explicitly, namely as r = 1.
> polarplot( 1, theta=0..2*Pi, scaling=constrained );
1 0.5 –1 –0.5 –0.5 –1 0.5 1 Use the scaling=constrained option to make the circle appear round. Here is the graph of r = sin(3θ).
> polarplot( sin(3*theta), theta=0..2*Pi ); 0.4 0.2 –0.8–0.6–0.4–0.2 0 –0.2 –0.4 –0.6 –0.8 –1 0.2 0.4 0.6 0.8 The graph of r = θ is a spiral.
> polarplot(theta, theta=0..4*Pi); 110 • Chapter 5: Plotting –5 8 6 4 2 –2 –4 –6 –8 –10 5 10 The polarplot command also accepts parametrized plots. That is, you can express the radius and angle coordinates in terms of a parameter, for example, t. The syntax is similar to a parametrized plot in Cartesian (ordinary) coordinates. See this section, page 106. polarplot( [ rexpr, angleexpr, parameter =range ] ) The equations r = sin(t) and θ = cos(t) deﬁne the following graph.
> polarplot( [ sin(t), cos(t), t=0..2*Pi ] ); 0.4 0.2 –1 –0.5 –0.2 –0.4 0.5 1 Here is the graph of θ = sin(3r).
> polarplot( [ r, sin(3*r), r=0..7 ] ); 5.1 Graphing in Two Dimensions • 111 4 2 0 –2 –4 1 2 3 4 5 6 Functions with Discontinuities
Functions with discontinuities require extra attention. This function has two discontinuities, at x = 1 and at x = 2. −1 if x < 1, 1 if 1 ≤ x < 2, f (x) = 3 otherwise. Deﬁne f (x) in Maple.
> f := x > piecewise( x<1, 1, x<2, 1, 3 ); f := x → piecewise(x < 1, −1, x < 2, 1, 3) > plot(f(x), x=0..3);
3 2 1 0 –1 0.5 1 1.5 x 2 2.5 3 Maple draws almost vertical lines near the point of a discontinuity. The option discont=true indicates that there may be discontinuities. 112 • Chapter 5: Plotting > plot(f(x), x=0..3, discont=true);
3 2 1 0 –1 0.5 1 1.5 x 2 2.5 3 Functions with Singularities
Functions with singularities, that is, those functions which become arbitrarily large at some point, constitute anothe...
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This note was uploaded on 08/27/2012 for the course MATH 1100 taught by Professor Nil during the Spring '12 term at National University of Singapore.
 Spring '12
 NIL
 Math, Division

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