Rigorous Gradient Tool | More applets |
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This Java applet computes the value and the gradient of a function at a
given point.

The function *f(x,y)* can be chosen freely, using the standard
arithmetic operations **+**, **-**, *****, **/**,
**^** (integer power) and the standard functions **sin**,
**cos**, **exp** and **sqrt**.
The point *(x,y)* at which the function is evaluated can also be chosen
by the user. Numerical constants are either floating point constants like
3.141, or intervals formed by such constants, for example [3.141, 3.142].
Intervals may also be used in the definition of the function.

- Evaluate the default function for different values of
*(x,y)*. In particular, choose intervals of different width, including width zero. - Change the function to
*f(x,y):=x-x*. Evaluate it at*x*=[1,2]. Surprised? This shows that two identical functions (*f=x-x*and*f=0*in our case), defined by different expressions, may evaluate to drastically different results. - Now change the function to
*f(x,y):=x*y*, and evaluate it for different values of*(x, y)*. Can you always predict the results? - Finally, define
*f(x,y):=x/y*, and evaluate it at*(x, y)*=(1, [-1,1]).

Last modified by Wolfgang Kühn on Sunday, 10 October 1999