Online tools
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One of many scientific calculators on the web. It accepts brackets, functions like
sin, cos, tan, exp, log, sqrt, pow, asin, acos, atan,
the constants E und PI.
On the calculator's web page you find a detailed description.
(The above version is loaded from the maths online website. Its original location is
there).
If you are not pleased with this calculator, you can choose out of
huge collections of
elementary and
powerful
complex
variants.
A handy calculator appearing in a small window.
It containts only a single input line, but it understands (almost) as many
statements as the JavaCalc calculator refered to above.
After typing in one or more functional expressions, the respective graphs are plotted.
The necessary calculations are taken over by the computer algebra systen
Mathematica.
Accordingly, the action of functions must be denoted by square brackets!
Funktions must be denoted as Sin or sin
(in Mathematica standard functions are written with capital first letter),
the symbol * for
multiplication may be omitted.
Example:
Sqrt[x] + x^2 Exp[-x], not Sqrt(x) + x^2 Exp(-x).
By the way: the plot is a gif-file and can be saved on your PC by a right
mouse click. It may be printed or included in other documents.
For a new plot, click the "Back"-button of your browser.
Type in a function and get its derivarive (or derivatives up to the order required)
in closed form.
The computation is taken over by the computer algebra systen
Mathematica.
Accordingly, the action of functions must be denoted by square brackets!
Funktions must be denoted as Sin or sin
(in Mathematica standard functions are written with capital first letter),
the symbol * for
multiplication may be omitted.
Example:
Sin[x] + x^2 Exp[-x], not Sin(x) + x^2 Exp(-x).
This page is a bit difficult to survey: The result is a web document looking
exactly like the input page. On its bottom side, below the heading
"The derivatives are:",
you find the required list of derivatives. In case of long expressions,
the symbol > means "to be continued next line".
A very useful tool: Type in a function and get its (indefinite) integral in closed form.
The computation is taken over by the computer algebra systen
Mathematica.
Accordingly, the action of functions must be denoted by square brackets!
Inputs are case-insensitive
(in Mathematica standard functions are written with capital first letter),
the symbol * for
multiplication may be omitted.
Example:
Tan[x] + x^2 Exp[-x], not Tan(x) + x^2 Exp(-x).
Type in a function and get its (exact) definite integral over the required interval.
The computation is taken over by the computer algebra systen
Mathematica.
Accordingly, the action of functions must be denoted by square brackets!
Funktions must be denoted as Sin or sin
(in Mathematica standard functions are written with capital first letter),
the symbol * for
multiplication may be omitted.
Example:
Cos[x] + x^2 Exp[-x], not Cos(x) + x^2 Exp(-x).
The program reckognizes divergent integrals quite well (e.g. over 1/x if 0 is in the integration
domain),
but a little bit of caution is in place!
The result appears at the bottom of a web document which otherwise looks like
the input page.
Computations with Mathematica
in the framework of the Maths & Fun
project at the
BHAK und BHAS Grazbachgasse in Graz (Austria):
This is the first Austrian server taking over your
Mathematica job.
You can choose between
The action of functions must be denoted by square brackets!
Funktions must be denoted as Sin or sin
(in Mathematica standard functions are written with capital first letter),
the symbol * for
multiplication may be omitted.
Example:
Cos[x] + x^2 Exp[-x], not Cos(x) + x^2 Exp(-x).
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Links ordered by topic
Numbers
Elementary geometry
Linear algebra
- Graphing Linear Equations
(applet) Learning program on linear functions and their graphical representation
as straight lines in a plane. Includes tutorial, test, quiz, crossword puzzle
and - as tools - the possibility to plot graphs of functions and a calculator.
You may pose questions to the teachers and discuss with pupils of the
Bremen High School, USA.
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Graph Applet (applet) A straight line may interactively be moved, the
coefficients m and b of its equation are shown.
- Java Script Linear Algebra
(JavaScript) Some pages about how to manipulate
3 x 3 matrices (multiply, invert,...)
and systems of linear equations in 3 variables.
A particularly useful tool is the
Java Script Linear Algebra Calculator. On
page III
systems of equations may be solved numerically.
The same author also offers a
Matrix Calculator Applet
capable of dealing with n x n matrices, and a short outline of the
mathematics behind
(also see his maths pages).
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Linear Equation Solver
(applet) Numerical Solution of systems of linear equations in
3 variables.
Vectors
Trigonometric functions and trigonometry
- Trigonometry (some applets)
A number of units to illustrate definitions, graphs and simple properties
of the trigonometric functions, including the
Sum Formulae, the Law of Sines and the Law of Cosines.
In particular see two applets about the graphs of the
Sine and the
Cosine function
and a further applet by which the definitions of the
various trigonometric functions may be compared.
Curves
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Famous Curves (graphics and applets)
More than sixty famous plane curves or families of curves
are discussed and represented graphically.
In the applet versions their parameters may be changed interactively.
See also the
Famous Curves Applet Index. (School of Mathematical and Computational Sciences,
University of St Andrews, Scotland).
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A Visual Dictionary of Special Plane Curves:
A lot of information on curves and families of curves.
Resources in various formats: images, Mathematica notebooks, Quick Time movies,
Sketchpad and Cabri files.
Integration
- Integration Applet (applet)
After typing in a function, the definite Integral is represented
graphically as area and its value is shown.
Probability and statistics
Numerical methods
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Bisection Method Tutorial (applet)
Illustates the bisection method to numerically solve equations of the form
f(x)=0 for some selected functions f.
- Numerical Integration Tutorial (applet)
Some methods for numerical integration are applied to a number of selected functions and
illustrated graphically in a nice way.
Fractals
Fourier analysis
- Realtime
Fourier sound synthesis (spreadsheet) Sound generator:
Determine the intensities of overtones by means of a scroll bar and listen to the according sound.
(Even without sound utility, the graphical side of this spreadsheet is a nice
illustration of the Fourier series).
History of mathematics
And...
Collections
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Mathematics Tools for School and Study
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Large list of multimedia learning material, provided
by Peter Krahmer from the University of Würzburg, Germany.
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- The Math Forum
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Erich Neuwirth's Spreadsite
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Here you find Excel spreadsheets on various mathematical and other
scientific topics by Erich Neuwirth (University of Vienna).
Along with an extensive collection of background material
and further links, the Spreadsite provides a good survey of
spreadsheet issues on the web.
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Mathematics Archives
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The Virtual Mathematics Center
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is part of the
Martindale's Graduate & Undergraduate Center: A
large list of multimedia resources on scientific issues is
provided by Jim Martindale, University of California, Irvine.
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Frank Potters's Science Gems - Mathematics
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is also a large list, sited at the University of California.
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- The Geometry Center
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at the University of Minnesota offers online learning material and
multimedia software.
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Cinderellas Café
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Interactive geometry on the computer, a software package from Germany.
Some demos are online.
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cabri géomètre
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is an interactive geometry software package from France. The homepage
offers informations about the product.
Cabri Java Applet contains some
online demos.
In cabri-java
you learn about the possibilities to combine this package with Java and
web technology.
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- School of the Web
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by M. Casco Associates, USA,
offers material about elementary topics of maths teaching and about
chaos theory and fractals.
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Math Education and Technology
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Offers from International Education Software, Japan.
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The MathServe Project
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Imagine the Imagined
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Interesting Java Applets
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on statistical issues. Institute of Statistics and Decision Sciences,
Duke University, USA.
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Ka's geometry page
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Maths Workshop
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Math Collections
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by Ken Kikuchi, Japan, the creator of the
online calculator refered to at the beginning of this page.
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MathsNet
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by Bryan Dye, Hewett School, England,
offers broad information about maths education and software,
in particular about Logo, spreadsheets and graphic calculators.
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Interactive Mathematics Miscellany and Puzzles
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by Alexander Bogomolny, University of Iowa,
offers information on numerous mathematical topics, enriched by interactive
material and mathematical games.
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Peter Alfeld's Home Page
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University of Utah, USA.
Good informations on maths topics and some applets, in particular one about the
Mandelbrot set.
Unfortunately, the applet is not easy to handle.
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Dr. Matrix' Web World of Science
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by Bruce Bowden, USA,
offers various kinds of material, among which you find mathematical
topics und
websites.
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- CAMEL
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the Web Service of the Canadian Mathematical Community)
offers many links to mathematical topics, e.g. (under
Knot a Braid of Links)
about numbers.
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The WWW Virtual Library - Mathematics
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provides general information on mathematics on the web and a
mathematical software index.
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The WWW Virtual Library - Statistics
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provides general information on statistics on the web.
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The Virtual Museum of Computing
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by Jonathan Bowen, University of Reading, England,
is part of the
Virtual Library museum pages,
a large web museum project. You find links to many topics relevant for mathematics,
with some emphasis on interactive material and the history of computing.
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Mathematics Resources
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a list provoded by the Rice School (Rice University und
The Houston Independent School District), USA.
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- Education Object Economy
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EOE is a project devoted to communication about Java applets, initiated by
Apple Computer.
You find some interesting maths learning tools.
(Type "mathematics" into the search engine at the bottom of the first page in order
to get the current status).
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- Fourmilab
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John Walker, the founder of Autodesk, offers his own software products,
together with a large collection of information on various scientific topics,
in particular on
Cellular Automata.
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- Introduction to Scientific Programming
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by Joseph L. Zachary, University of Utah, USA. The site
provides tutorials on different topics of numerical mathematics and some interactive material.
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Educational Interests
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"many of the best educational sites on the Internet",
collected by Wayne Summers, New Mexico Highlands University.
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Homework Helpers
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for pupils, provided by the WebAndStuff Mailing List.
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Maths teaching and the internet (Mathematikunterricht und Internet)
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Links to maths sites (Links zu Mathematik-Sites)
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provided by the University of Klagenfurt, Austria.
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Mathematical links on the web (Mathematische Links im WWW)
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provided by the University of Ulm, Germany.
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Web resources for maths education (
Mathematikresourcen für den Unterrichtsgebrauch im Internet)
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an introduction by Hannes Kaufmann, University of Vienna.
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World Wide Sources for Mathematics Teaching
(Weltweite Quellen zum Mathematikunterricht)
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collected by the Center for Teaching Media on the Web
(Zentrale für Unterrichtsmedien im Internet), Germany.
A lot of information on mathematics software and online material.
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Mathematical Games, Toys, and Puzzles
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Rich collection by Jeff Erickson, Duke
University, USA.
Unfortunately, the page has not been updated for a long time, so that
many links are already out of date.
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Eric's Treasure Trove of Mathematics
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Glossary of mathematical notions
by Eric W. Weisstein, University of Virginia, USA.
Also see the extensive list of maths links on his
homepage.
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Maths & Fun
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DERIVE - Texts on the web (Texte auf dem Internet)
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an initiative devoted to the use of the computer algebra system
DERIVE in Austrian schools.
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- The Connected Curriculum Project
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by Frank Wattenberg, Montana State University,
offers online help for the calculator TI-92, the computer algebra systems
Mathematica und Maple and the programming language Java. You also find
applets and further information on mathematical issues.
(A description of TI-92 may also be found here).
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