Modelling
with functions - the data sets page includes
links to data sets.
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Modelling
with functions - the data sets page includes
links to data sets.
National
Library of Virtual Manipulatives for Interactive Mathematics
Mathematics
Used In Technology
applications
of Mathematics to various areas of technology
Project-Based
Instruction in Mathematics for the Liberal Arts
applications
of linear and non-linear functions
algebra
popup tools - WWW Interactive Server
Expand, factorise, simplify, solve
equations.
QuickMath
graph plot
graphing
popup tools - WWW Interactive Server
MathServ
Calculus Toolkit
wide variety of calculators and
plotters for algebra and calculus (includes polar and parametric graphs)
Winplot
software / Winplot
Tutorial
Eigenmath
software - George Weigt
symbolic algebra
and calculus
Factoris
Factorise an integer, rational number,
polynomial or rational function.
How
does my pattern grow?
Make the next
picture. Find a rule?
Paul
McCartney's Maths Book
two pages of algebra by Paul McCartney
x^3
- y^3
function
notation and the graph
addition
of functions
Recognise the graph of f(x)+g(x)
...
multiplication
of functions
Recognise the graph of f(x)g(x)
...
composition
of functions - software
This slide
show shows how f(g(x)) can be constructed graphically from the graphs of
f(x) and g(x). It also shows how the chain rule f(g(x))'=f'(g(x))g'(x)
can be obtained graphically using this construction.
inverse
function
Recognise the graph of f -1(x)
...
transformation
of graphs
Recognise the graph of f(-x), 2f(x),
f(x-1) ...
arithmetic
series
demonstration of the formula for
the sum of an arithmetic sequence
infinite
geometric series
Baravelle Spirals are generated
by connecting the midpoints of the successive sides of a regular polygon.
The sum of an infinite geometric sequence is illustrated by the triangles
formed.
sequence
plot - WWW Interactive Server
plot numerical sequences and series
up to 1000 terms
gas
laws
Investigate relationships - pressure,
volume, temperature, ... - includes graphs.
behaviour
of Northwestern Crows
Northwestern crows drop a type of
mollusk called a whelk in order to break the shell. Model this behaviour
with a rational / reciprocal function.
Pendulum
- investigate relationships between period and the length or the gravitational
acceleration. Version 2 also makes allowance for the effect of the initial
amplitude.
polynomial
functions - Maths Online
interpolation
polynomials
Fit a polynomial function to a number
of points.
scaling
- power functions in nature (M=axk)
Hanging
with Galileo - Paul Kunkel
Gateway
Arch
catenary equation and other information
for the Gateway Arch in St. Louis
Famous
Curves - MacTutor History Archive
history, links to Java applets
Visual
Dictionary of Special Plane Curves - Xah Lee
descriptions, properties, graphics,
animations, links
Curves
- Paul Bourke
classical curves, Cassini ovals,
knots, ...
cycloid
/ logarithmic spiral generator - Maths Online
roller
coasters and the cycloid
One-half of a cycloid upside-down
gives the roller coaster's track that will yield the shortest possible
time for the ride.
rose
curves - Xah Lee
a study of curves with polar equation
r = a cos(p/q*theta)
x(t)=(R+r)cos(t) - p*cos((R+r)t/r) , y(t)=(R+r)sin(t) - p*sin((R+r)t/r)Use sliders to change:
R - radius of the circle with centre at the originValues are given for a cardioid, astroid, rose, vertical line, ellipse, spiral, ... (applet can be downloaded).
r - radius of the circle that rolls around the outside (r>0) or inside (r<0) of the first circle
p - distance of the point from the centre of the moving circle
Mygalomorph
Geometry Explorer
cardioid, nephroid, ranunculoid
and other curves
parametric
equations plotter (x(t), y(t))
parametric
equations plotter (x(t), y(t)) with animation
Create gif animations of graphs
- example of unit circle
x(t)=cos(t), y(t)=sin(t).
parametric
equations of circles, ellipses and Lissajou figures - R.F.Barrow
plotter for x=Acos(Bt) and y=Csin(Dt)
Cubic
spline and Bezier curves - Consider the end point (a,b) and its control
point (c,d) and the end point (g,h) and its control point (e,f). The spline
curve is given by the parametric equations:
3D
Surface Viewer - Bright Ideas Software
3
dimensional graph plotter z=f(x,y)
gallery
of 3 dimensional surfaces - pictures and equations
wind
chill index - Meteorological Service of Canada
wind chill index as a function of
air temperature and wind speed, calculator, charts and tables
Line
Designs and Curve Stitching - collection of links - Jill Britton
learning
resources and sources of problems