# 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.

Return to the SLU Math Applets
page.

Return to the Saint Louis University Department of Mathematics and Computer Science
home page

Last updated by Mike May, S.J. on
October 6, 2006.