List of useful links
 to online tools




Maths links - Survey


This page contains prepared links to more than sixty online tools for every day purposes, and some hints where you find more. Some selected links which will be used very often (on account of their generality) are designed as buttons. Below these you find a list of more specialized tools. Each tool is started in its own browser window, so that it may be used simultaneously with other pages of maths online.

For a refined search on this page use your browser's search functionality (Menu Edit Find in Page or the key combination Ctrl F)!



Online tools
 
      JavaCalc - Calculator
One of many scientific calculators on the web. It accepts brackets, functions like sin, cos, tan, exp, log, sqrt, pow, asin, acos, atan, gamma, the constants E und PI. On the calculator's web page you find a detailed description. In a cooperation between the author and maths online in the beginning of 2000, the calculator's functionality has been extended. (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.


      maths online mini-calculator
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.


      Solving equations
The computer algebra system Mathematica carries out the necessary computations exactly and numerically. (The equation may contain symbolic constants. Although the page offers only the solution of polynomial equations, some more general equations are admissible too). The symbol * for multiplication may be omitted. The result appears at the bottom of a web document which otherwise looks like the input page.


      Solving systems of equations
The computer algebra system Mathematica carries out the necessary computations exactly. (The equations may contain symbolic constants). The symbol * for multiplication may be omitted. The result appears at the bottom of a web document which otherwise looks like the input page.


  Eigenvalues eigenvectors matrix
The computer algebra system Mathematica carries out the necessary computations. (The matrix may contain symbolic constants). The symbol * for multiplication may be omitted. The result appears at the bottom of a web document which otherwise looks like the input page.


      maths online function plotter
After entering one or more functional expressions, the graphs are drawn. Using the zoom option, you may study the graphs from a very "close" viewpoint and read off coordinates of interesting points with an accuracy of about 10-14. (Java applet; part of the program is the parser by Darius Bacon).


      Plotting function graphs
After typing in one or more functional expressions, the respective graphs are plotted. The necessary calculations are taken over by the computer algebra system Mathematica. The action of functions may be denoted by square brackets (Mathematica sytnax) or round brackets. Funktion names must be denoted as Sin or sin. The symbol * for multiplication may be omitted.
Example: Sqrt[x] + x^2 Exp[-x] or 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.
 

      Numerical computation of sequences
After typing in an expression for an, an initial value, an upper bound and a step-width, the items of the sequence are represented numerically.
 

      Numerical computation of series
After typing in an expression for ak, the items of the sequence of partial sums are represented numerically.


      Derivative of a function
Type in an expression defining a function and get its derivarive (or derivatives up to the order required) in closed form. The expression may contain symbolic constants. The computation is taken over by the computer algebra systen Mathematica. The action of functions may be denoted by square brackets (Mathematica sytnax) or round brackets. Funktion names must be denoted as Sin or sin. The symbol * for multiplication may be omitted.
Example: Sin[x] + x^2 Exp[-x] or 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".


      The Integrator
A very useful tool: Type in an expression defining a function and get its (indefinite) integral in closed form. The expression may contain symbolic constants. The computation is taken over by the computer algebra systen Mathematica. Here, the action of functions must - according to the Mathematica syntax, 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).


      Definite Integral
Type in an expression defining a function and get its (exact) definite integral over the required interval. The expression may contain symbolic constants. The computation is taken over by the computer algebra systen Mathematica. The action of functions may be denoted by square brackets (Mathematica sytnax) or round brackets. Funktion names must be denoted as Sin or sin. The symbol * for multiplication may be omitted.
Example: Cos[x] + x^2 Exp[-x] or cos(x) + x^2 exp(-x).
The program recognizes 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.


This tool may help you to get mathematical symbols on a web page, provided you know a little bit about HTML. It comes with a detailled description. You may download it and use it on a local computer (without web connection).
Further information on this topic may be found on the page Formulae and the web.





The MathServe Project at the Vanderbilt University, USA, provides useful online tools on many topics, most of them relying on the computer algebra system Mathematica and are thus capable of performing exact computations. Some of the tools given above stem from this collection. At the page The MathServ Calculus Toolkit you find applications on algebra and analysis, among which are:
The page The MathServ DE Toolkit offers tools on differential equations, among which are:


The page Maths by Internet (Mathematik mit Hilfe des Internets) collects some Java based online tools developed at the University of Bayreuth (Germany):


Numerical tools on linear algebra:


Computer algebra systems (CAS) are able to perform symbolic and numeric computations, simplify expressions, solve equations and differential equations, plot function graphs, differentiate, integrate, and much more. On the web, CAS may be found at the following sites.


Dynamical geometry on the web may be found at the following sites. For more information on the first four items in the following list see our page collections.


Hint for those who want to create their own mathematical web sites: JGV: 3D Viewing in Java offers an applet which generates movable 3D objects.


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