Using Maple in 13.1 and 13.2: We'll need the VectorCalculus and plots packages, so we'll load those first with(VectorCalculus): with(plots): In the first example, plot a space curve whose representating is given in parametric form: < t^2-1, t+1, t^3+1 > Unlike in two dimensions, the t values go outside the brackets... After you plot, notice that you can click on the figure and rotate the curve around. spacecurve([t^2-1,t+1,t^3+1], t=-3..3, color=black); In this example, we'll add in the projections to the xy-plane spacecurve({[t^2-1,t+1,t^3+1],[t^2-1,t+1,0]},t=-3..3,color=black); Example: Plot two surfaces and the curve of intersection Eqn1:=1-x-y; Eqn2:=x^2+y^2; xt:=sqrt(3/2)*cos(t)-1/2; yt:=sqrt(3/2)*sin(t)-1/2; Param:=[xt,yt,1-xt-yt],t=0..2*Pi; A:=plot3d({Eqn1,Eqn2},x=-3..3,y=-3..3,style=surfacewireframe); B:=spacecurve(Param,color=black,thickness=3); display(A,B); Example using a limit: R:=<exp(-3*t), (t^2/sin(t)), cos(2*t)>; limit(R,t=0); Example using the derivative. For the second derivative, you can either differentiate the derivative or tell Maple to compute the second directly (dollar sign is used) R:=<t^2,t,cos(t)>; dR:=diff(R,t); d2R:=diff(dR, t); d2R:=diff(R,t$2); # Compute the second derivative directly Tangent Line example: Plot a curve with its tangent line: xt:=4*sqrt(t); yt:=t^2; zt:=t; r:=<xt,yt,zt>; dr:=diff(r,t); r1:=subs(t=1,r); # Point for the line r2:=subs(t=1,dr); # Direction for the line Line1:=r1+t*r2; spacecurve({r,Line1},t=-3..3,color=black); # Plotting two space curves together. How to compute a unit tangent vector, T(t): T:=TangentVector(r, normalized); We can integrate a vector valued function: int(r,t); or integrate with bounds: int(r,t=0..1); We can check the formula: (r x r' )' = r x r'': R1:=diff(CrossProduct(r, diff(r,t)),t); R2:=CrossProduct(r, diff(r,t$2)); Solve for a point of intersection between the lines leads to a system of equations like the following, which we solve: t=3-s, 1-t=s-2, 3+t^2 = s^2 solve({t=3-s, 1-t=s-2, 3+t^2=s^2}, {t,s});