Student Package

The student package is a collection of special tools to help visualize and understand a few of the concepts in Calculus. I find that Maple's student package provides an excellent tool to help students appreciate Riemann sums.

> with(student);

> f := x -> x^3-6*x^2+9*x+2;

The student package makes it easy to view a tangent line.

> showtangent(f(x),x=4,x=0..5);

Riemann Sums

The next series of commands allow one to see the formulae and the geometric interpretation of the Riemann sums as they converge to the value of the integral.

> middlesum(f(x),x=0..5,5);

> evalf(%);

> middlebox(f(x),x=0..5,5);

> middlesum(f(x),x=0..5,10);

> evalf(%);

>

> middlebox(f(x),x=0..5,10);

> middlesum(f(x),x=0..5,20);

> evalf(%);

>

> middlebox(f(x),x=0..5,20);

> middlesum(f(x),x=0..5,40);

> evalf(%);

>

> middlebox(f(x),x=0..5,40);

> int(f(x),x=0..5);evalf(%);

> Int(f(x),x=0..5);