1. Plotting functions and formulas

We can plot functions and formulas without explit conversions:

>	formula := exp(-x^2)*sin(Pi*x^2);

>	plot(formula,x=-2..2); # x is the independent variable

>	f := unapply(formula,x):

>	plot(f(t),t=-2..2);  # plotting via a conversion to formula

>	plot(f,-2..2); # no need to specify x

2. Displaying and animating plots

Maple has datastructures for plots.  The plot command from above proceeded in two steps:

1. create the plot; 2. rendering the plot.  If we assign the plot to a variable, we can separate these two stages.

>	p1 := plot(formula,x=-2..2); # creation of the plot, stored in p1

Note that we better terminate with a : instead of the semi-colon...

>	display(p1); # rendering of the plot

The display can handle multiple arguments.

>	p2 := plot(subs(Pi=2*Pi,formula),x=-2..2,color=green):

>	display(p1,p2);

Instead of putting p1 and p2 on the same plot, we can put them after each other:

>	display(p1,p2,insequence=true);

Suppose we would like an animation of 20 frames, for increasing values of the factor in front of the Pi, i.e.:  p1 is for 1*Pi, p2 is for 2*Pi, in general p[k] will be for k*Pi.

>	pl := seq(plot(subs(Pi=k*Pi,formula),x=-2..2),k=1..20):

>	display(pl,insequence=true);

>

3. Plotting around singularities

We can plot algebraic curves, defined by one polynomial in two variables.

>	curve := x^3 + y^3 -5*x*y + 1/5;

>	implicitplot(curve,x=-3..3,y=-3..3,numpoints=5000);

>	watt := (x^2+y^2)^3 + 5.12*(x^2+y^2)^2 - 5.15*(x^4-y^4) - 14.7456*y^2;

>	implicitplot(watt,x=-3..3,y=-3..3,numpoints=10000);

By taking enough samples we can get a faithful plot.  The problem is the singularity at the origin, at (0,0), which we can resolve via polar coordinates.

>	polar_watt := subs(x=r*cos(t),y=r*sin(t),watt);

>	s := solve(polar_watt/r^2,r);

The solution give us parameterization r as a function of t, for this curve.

>	polarplot(s[1],t=0..Pi);

>

4. Sparse Matrices

see lecture note

5. Curve Fitting

see lecture note