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

Adding points in ℝ² (Desmos link)

Scaling points in ℝ² (Desmos link)

Parameterizing lines in ℝ² (Desmos link)

Linear combinations / graphical linear equation solving in ℝ² (Desmos link)

Length in ℝ² (Desmos link)

Coordinates and graphs of points in ℝ² (Desmos)

Point-testers vs. point-generators (Desmos)

Rectangular [Cartesian] coordinates in space (ℝ³)

Adding points in space (ℝ³)

Associativity of addition of points in ℝ³

Scaling and spans in ℝ³(various cases)

Linear combinations / graphical linear equation solving in ℝ³

Length and direction in ℝ³

Translation in ℝ² (Desmos link)

Translation in ℝ³

Vector parameterizations of lines in ℝ³

Spans of pairs of vectors in ℝ³

Spans of triples of vectors in ℝ³

Equivalent vectors in ℝ, ℝ², and ℝ³

Arrows and vectors in ℝ²

Length, direction, unit vectors, and normalization in ℝ² (Desmos link)

Length, direction, unit vectors, and normalization in ℝ² (Desmos link)

Pythagorean theorem and distance in ℝ³

Length, direction, unit vectors, and normalization in ℝ³

Orthogonal decomposition

Gaussian elimination sketchpad

Shifting and scaling functions (Desmos link)

Composition visualized via projections (Desmos link)

Review of basic trigonometry functions highlighting meaning of "co" (Desmos link)

Graphical view of a couple of fundamental trigonometric inequalities (Desmos link)

Objects in free fall and average speed (Desmos link)

Slopes of secants and average rate of change (Desmos link)

Limits of secant lines and rates of change (Desmos link)

Informal introduction to limits (Desmos link)

Graphical view of ε-δ limit formal limit definition (Desmos link)

Limit of difference quotient vs. limit of derivative (Desmos link)

Weierstrass everywhere continuous nowhere differentiable function (Desmos link)

Graphical perspective on inverse functions (Desmos link)

Newton's method for approximating zeros of differentiable functions (Desmos link)

Bisection method for approximating zeros of continuous functions (Desmos link)

Parametric equations for curves in ℝ² and ℝ³

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

Level curves for a discontinuous function of two variables

Limits vs radial limits for functions of two variables

Limits vs radial limits for functions of two variables (Desmos version)

Radial limits for functions of two variables, another example (Desmos)

Constrained optimization

Stress tensor visualization and exploration tool

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

Unit tangent and unit speed parameterizations

Curvature and normal vectors of a curve

Tangential and normal components of acceleration

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 12/26/2025.