Help for Banchoff Applets

Available Functions and Syntax

This page looks at issues of interest to a user of configured Banchoff Applets. Someone wanting to create their own applets will need more information and should contact the author of this page.

The three sections of help are:
Controlling the view of graphical windows
The Control Window and the kinds of controls in that window
Functions recognized by the applet

Functions recognized by the parser in the applet

Basic functions
Differentiations and integration
Functions on vectors
Functions on variables and intervals
Non-standard functions
Logical operators

Basic functions

As a general rule, functions are typed into the applet uses standard calculator syntax.
The standard math functions are available with the usual syntax:
+, -, *, /, ^, abs, ln, sqrt, sin, cos, tan, asin, acos, atan, sinh, cosh, tanh.
The standard math constants e and pi are also available.

Differentiation and integration

The applet computes derivatives symbolically.
Derivatives of a function of one variable use the prime notation.

f '(x), read f prime of x, is the first derivative of f(x) with respect to x.
f ' '(x), read f prime prime of x, is the second derivative of f(x) with respect to x.

Partial derivatives use the subscript notation.

f_x is the partial derivative of f with respect to x.
f_x_y is the second partial derivative of f, first differentiating with respect to x, then with respect to y.

Integration is approximated numerically with Simpson's rule.

integral (f(x),x,a,b,res) estimates the integral of f(x) with respect to x from a to b using Simpson's rule with res intervals.
integral (f(x),x,a,b) estimates the integral of f(x) with respect to x from a to b using Simpson's rule with 10 intervals.

Functions that operate on vectors:

length(v) - Returns the length of the vector v.
dot(v,w) - Returns the dot product of the vectors v and w.
cross(v,w) - Returns the cross product of the vectors v and w.
unit(v) - Returns the unit vector in the same direction as the vector v.
component functions: v_1 returns the first component of v, while v_2 returns the second component of v, etc.

Functions that operate on variables or intervals:

_max - t_max is the maximum value of t.
_min - t_min is the minimum value of t.
_res - t_res is the number of steps in t.
scale - scale(t) converts the value of t to a point in the 0-1 range.

Nonstandard functions:

ipart - Returns the integer part of x. ipart(-1.7)=-1.
fpart - Returns the fractional part of x. fpart(-1.7)=-.7.
max - Returns the maximal element of a set. max(2,3,4)=4.
min - Returns the minimal element of a set. min(2,3,4)=2.
random - Returns a random number between 0 and 1. Takes no argument.

Logical operators :

These functions return a value of 1 if true and 0 if false.
and, or, < , > , =, true, false.
For example, (2<2)=0 while ((2<2)or(2=2))=1.

Return to the SLU Banchoff Applets page.
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Last updated by Mike May, S.J. on October 6, 2006.