List of useful links
 to online tools and
 mathematical subjects






On this page you find some selected links which are relevant for learning and teaching of mathematics: First
  • Online tools, which may be used for various purposes. (Any tool is started in its own browser window so that it may be used simultaneously with any other web page). Then
  • Links ordered by topic, where we have laid emphasis on interactive learning material which needs no download or additional software. (We have included some spreadsheets which can be started if you have installed Microsoft Excel on your computer). And, last but not least,
  • Collections, inviting the user to explore the web and make his or her own discoveries.



 
Online tools

 
 
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

   

or just use a free

.

The graphics are gif-files and can be saved on your PC by a right mouse click. They may be printed or included in other documents.

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).


 
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.
  • 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).
  • 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
  • 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).
  • 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
  • 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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