?plottingguideThis one source of information is recommended, because it can resolve issues about what to do in order to obtain the desired plot. Memorize

# STANDARD COORDINATES # Maple can construct many kinds of graphs, a feature that you can use to # visualize mathematical objects and processes. The command plot( sin(3*x), x = -Pi..Pi ); # produces a plot containing the curve y = sin(3 x) for x in the # interval from -Pi to Pi. # No space is allowed between the double-dots in a plot command. Scales # on the x-axis and y-axis are chosen in the maple engine. To change # this behavior: plot( sin(3*x), x = -Pi..Pi, scaling = constrained ); # Sometimes it is useful to restrict the range over which y varies. We # get a misleading graph from plot( tan(x), x = -5..5 ); # It does not accurately represent the vertical asymptotes of y = tan(x). # Better results are obtained with plot( tan(x), x = -5..5, y = -2..2 ); plot(tan,-5..5,-2..2); # Same result with less typing # MULTIPLE CURVES ON ONE PLOT # To plot y = sin(x) and y = sin(3 x) one a single axis, code plot( { sin(x), sin(3*x) }, x = -Pi..Pi ); # The curve equations are inside set-delimiters of curly braces # You can also use square brackets, helpful for assigned colors. plot([sin(x),sin(3*x)],x = -Pi..Pi,color=[red,blue] ); # Decimal points can conflict with double-dot range parsing plot(1+x^2,x=1 .. 0.8); # Compare syntax x=1...8 # THE PLOTS PACKAGE # The DISPLAY command is found in the PLOTS package. # It allows you to assemble several plots onto one set of axes. with(plots): plot1 := plot(x^2,x=0..4): # Colon to omit graphic display plot2 := plot(3*x^2-2,x=0..4): display([ plot1,plot2]);

# PARAMETRIC EQUATIONS # A curve in the plane can be described as the graph of a function, as in # the graph of # 1 / 2\ # y = - sqrt\4 - x / # 2 # for x in the interval from -1 to 1. It can be given parametrically as # # (x(t), y(t)) = (2 cos(t), sin(t)) # # for t in the interval from 0 to Pi. Often we interpret such a curve as # the path traced by a moving particle at time t . Use the plot command # to draw a curve from this parametric description: plot( [2*cos(t), sin(t), t = 0..Pi] ); # unconstrained, distorted graphic plot( [2*cos(t), sin(t), t = 0..Pi], scaling = constrained); # constrained is not distorted # POLAR COORDINATES # Polar plots are a special kind of parametric plot. The polar # coordinates ( r, theta ) of points on a curve can be given as a # function of some parameter t. In many cases the parameter is just the # angle theta. Consider the ellipse defined in standard coordinates by # # x^2 + 4 y^2 = 4 # # To find an equation relating the polar coordinates r and theta of a # typical point on this ellipse, we make the substitution x = r cos(t) # and y = r sin(t), where t = theta. subs( x = r*cos(t), y = r*sin(t), x^2 + 4*y^2 = 4); simplify( % ); solve( %, r ); # We find that the ellipse is the collection of points whose polar # coordinates ( r, theta ) satisfy # # 2 4 # r = -----------------, # 2 # 4 - 3 cos(theta) # # and the following commands draw the right half of the ellipse: r := 2/sqrt( 4 - 3*cos(t)^2 ): plot( [ r, t, t = -Pi/2..Pi/2 ], coords = polar ); # Here are some more of examples of polar plots that you can try: plot( [ 1, t, t = 0..2*Pi], coords=polar ): plot( [t, t, t = 0..2*Pi], coords=polar ): plot( [ sin(4*t), t, t = 0..2*Pi], coords=polar ): # a more realistic picture is obtained with scaling = constrained. # PLOTTING RAW DATA # Maple can plot data consisting of pairs of x and y values. For # example, the double list data := [ [0, 0.53], [1, 1.14], [2, 1.84], [3, 4.12] ]; # defines data as a sequence of five data points. # A double list is something enclosed in square brackets, with # comma-separated elements in square brackets. Lists are used # for collections of objects where the order matters. data[1]; data[2]; data[3]; data[4]; # Individual items are accessed this way data[3][2]; # Extract 2nd coordinate 1.84 from the 3rd data point [2,1.84] # To plot the points in a double-list we use commands like plot(data); # The simplest interface to plotting points. plot(data,opts); # Plot with an option definition like opts:=style = point, symbol = circle, color = black; opts:=style = line, view = [0..4, 0..5]; opts:=style = line, title = "Experiment 1"; # The double quote is used to specify a plot title string. See # ?plot[options] for more information, e.g., about symbols and line # styles available. See ?plottingguide for ideas and examples. # Display help ?readdata and ?writedata to find out how # to read or write a file of data points into a Maple session.

# EXAMPLE. Graphing functions of two variables. f:=(x,y)->x^2-y^2; plot1:=plot3d(f(x,y),x=-1..1,y=-1..1,color=blue): # Graph of z=x^2-y^2 plot2:=plot3d([.5*cos(theta),.5*sin(theta),z], theta=0..2*Pi,z=0..1,color=pink): # Graph of a cylinder, defined parametrically plot3:=plot3d(.5,x=-1..1,y=-1..1,color=brown): # A horizontal plane z=0.5 with(plots): display([plot1,plot2,plot3],axes=boxed); # Click on the plot to move it around in space. # A box in upper left of window will display # the spherical coordinates you're looking from! # EXAMPLE. Implicit plots. with(plots): f:=(x,y)->x^2-y^2; implicitplot(f(x,y)=.5,x=-1..1,y=-1..1,color=black); # The level curve where x^2-y^2=.5 with(plots):g:=(x,y)->3*x^2-2*x*y+5*y^2: # A quadratic function of two variables implicitplot(g(x,y)=1,x=-2..2,y=-2..2,color=blue,grid=[80,80]); # Default grid unappealing, needed better resolution.