This Java applet computes the value and the gradient of a function at a given point.

Description

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.

Tutorial

• 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]).