# Available Functions and Syntax

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.