Web Links
The web contains a plethora of interesting resources to help you visaulize
important mathematical concepts -- the following is a selection of some of
my favorites that pertain to 18.01 (and are also fun to play with).
The list may be updated as I find more.
Most of these are Java applets, which run interactively
as plug-ins in your web browser.
To use them you must have Java enabled in your browser preferences --
by default, it probably is already.
- Some Java applets from MIT's OpenCourseWare page for 18.013A:
- Function
and Derivative Animations, by Przemyslaw Bogacki and Gordon Melrose (.avi
files, can play e.g. with
Windows
Media Player)
- Java applets of secant lines and tangent lines (from IES,
Manipula
Math):
- Secant lines
for a function with two non-differentiable points (applet by
Daniel J. Heath)
- Animations of secant lines approaching (or not approaching) tangent lines
(by Douglas N. Arnold):
- Constructing
functions that are continuous but nowhere differentiable(!), applet
from Maths Online
- Chain rule applet (from a
multimedia calculus course
by Scott Sarra)
- First
and second derivatives applet (by Scott Sarra)
- More first and second derivatives, with parameters
you can tweak (applet
from Maths Online)
- Derivatives of
ax,
sin x,
cos x
(applets by Daniel J. Heath)
- Converging
to the number e (applet from IES,
Manipula
Math); note that the simulation doesn't let you go far enough to
approach that close to e
- Zooming
in on a tangent line (animation by Douglas N. Arnold)
- Linear
approximation of sin x at 0 (applet from
UBC Calculus Online)
- Finding
a function's extremum, applet
from Maths Online
- Rolle's
theorem and the mean value theorem (applet from
IES, Manipula
Math)
- Some nice integral applets (by Daniel J. Heath):
- Numerical
Integration Simulation (by Joseph L. Zachary)
- Some applets on volumes of solids
(from IES, Manipula
Math):
- Direction
field applet (by Scott Sarra)
- More
direction field applets
(from UBC Calculus Online)
- Yet
another direction field applet
(from IES, Manipula
Math)
- Parametric
equation applet (by Scott Sarra)
- Another
parametric equation applet (from IES,
Manipula Math)
- Cycloid
animation (by Przemyslaw Bogacki and Gordon Melrose)
- Cycloid
applet (from Maths Online)
- Computing arc
length (animation by Przemyslaw Bogacki and Gordon Melrose)
- Approximating
arc length (applet by Daniel J. Heath)
- Polar
curve applet (from IES,
Manipula Math)
- Several polar curve animations (by Przemyslaw Bogacki and Gordon Melrose):
- Converging and diverging series animations (by Przemyslaw Bogacki and Gordon Melrose):
- Numerical
tools for computing sequences / series (from Maths Online)
- Taylor approximations
(applet by Daniel J. Heath)
- Power
series grapher
And just for the hell of it, there's the
Quadratic
Formula Song.