Interactive tools, activities, and demos

General notes about the toolkit

Requisites
Hardware / software requirements
Interface
User interface conventions
Settings
Adjust settings
Bugs
Known bugs
Acknowledgments
A few words of appreciation

Toolkit directory

Projections
Orthogonal decomposition
Parametric curves
Parametric equations
Arclength
Arclength of function graph
r'
Difference quotients of vector valued functions
Polar coordinates
Introduction to polar coordinates
Polar plots
Introduction to polar plots
Area in polar
Computing areas using polar coordinates
Work
Computing work
Lagrange multipliers
Constrained optimization

Discussion notes and demos

Parametric eqn's
Introduction to parametric equations
Parametric calculus
Calculus with parametric equations
Curves in space
Curves in space and their tangents
Parametric arclength
Arclength of curves defined parametrically
Speed
Speed of trajectories defined parametrically
Arclength (again)
Arclength of function graphs
Area
Computing area
Volume
Computing volume
Shell method
Computing volume by the shell method
Definite integrals
Setting up a definite integral
Surface area
Areas of surfaces of revolution
Work
Work and fluid forces
Moments
Moments and centers of mass
Polar coord's
Polar coordinates
Polar graphing
Plotting in polar coordinates

Videos

Circular motion
Variable speed circular motion
Challenge
Can you parameterize the curve?
Volume
Volume by cross section
Taylor polynomials
Sequence of Taylor polynomial approximations
Fourier series
Sequence of trigonometric polynomial approximations
Generalized cylinder
Profile curve and rulings of a generalized cylinder
Hyperboloids
Hyperboloids and cross sections
exp: ℂ ➝ ℂ
Complex exponential function
Möbius transformations
Parabolic, hyperbolic, and elliptic Möbius transformations
Dirichlet polygons
Dirichlet polygon animation

Please feel free to send me comments, questions, and bug reports at .

These pages were last updated on 1/22/2024.