Interactive tools, activities, and demos

General notes about the toolkit

Hardware / software requirements

User interface conventions

Adjust settings

Known bugs

A few words of appreciation

Orthogonal decomposition

Parametric equations

Arclength of function graph

Difference quotients of vector valued functions

Introduction to polar coordinates

Introduction to polar plots

Computing areas using polar coordinates

Computing work

Constrained optimization

Introduction to parametric equations

Calculus with parametric equations

Curves in space and their tangents

Integrals of vector functions and projectile motion

Arclength of curves defined parametrically

Speed of trajectories defined parametrically

Arclength of function graphs

Arclength of parametric space curves

Review of basic vector operations

Computing area

Computing volume

Computing volume by the shell method

Setting up a definite integral

Areas of surfaces of revolution

Work and fluid forces

Moments and centers of mass

Polar coordinates

Plotting in polar coordinates

Computing area in polar coordinates

Videos

Variable speed circular motion

Can you parameterize the curve?

Volume by cross section

Sequence of Taylor polynomial approximations

Sequence of trigonometric polynomial approximations

Profile curve and rulings of a generalized cylinder

Hyperboloids and cross sections

Complex exponential function

Parabolic, hyperbolic, and elliptic Möbius transformations

Dirichlet polygon animation

Please feel free to send me comments, questions, and bug reports at robert.smyth@cooper.edu or rwscu@tutamail.com.

These pages were last updated on 1/29/2025.