Functions

The use of this tool is illustrated in the examples The Derivative and The Spiral.

The configuration panel of FUNCTIONS may have as many lines as desired. Each line defines a function and looks like this:

f=sin(x)+sin(2*x-1)+cos(pi*x)

FUNCTIONS are function of one real variable and must be defined with x as the variable. The definition of a function may include constants, parameters, variables, arithmetic operations and the most common mathematical functions (trigonometric, inverse trigonometric, exponential and logarithmic functions). It is not allowed to use other functions defined in previous lines.

functions may be used to define equations. The evaluation of   functions is not as efficient as that of  variables. For this reason the indiscriminate use of functions may result in very slow graphs. The user should use  VARIABLES instead of FUNCTIONS wheneve possible. However the use of functions is indicated or even necessary, for example, when a function is repeatedly used in the graphs, when the function must be   evaluated in arguments not equal to x like in f(2-x), or to simplify the expression with which an equation is defined.

The following example shows how a function may be used to illustrate the translation of the graph of an "arbitrary" function. The function f used in the example is defined internally and the student only sees the "abstract" expression y=f(x-a).

Mathematical Functions and Operators.

These are the mathematical functions recognized by the expression analyser of Descartes:

sqr          sqr(x)=x*x
sqrt        sqrt(x)=square root of x
exp         exp(x)=exponential of x=e^x
log         log(x)=natural logarithm of x
log10       log10(x)=base 10 logarithm of x
abs         abs(x)=absolut value of x
ent         ent(x)=largest integer n such that n<x
sgn         sgn(x)=sign of x (1 if x>0,-1 if x<0,0 of x=0)
ind         ind(b)=indicator of b (1 if b=true, 0 if b=false)
sin         sin(x)=sine of x
cos         cos(x)=cosine of x
tan         tan(x)=tangent of x
cot         cot(x)=cotangent of x
sec         sec(x)=secant of x
csc         csc(x)=cosecant of x
sinh        sinh(x)=hiperbolic sine of x=(exp(x)-exp(-x))/2
cosh        cosh(x)=hiperbolic cosine of x=(exp(x)+exp(-x))/2
tanh        tanh(x)=hiperbolic tangent of x=sinh(x)/cosh(x)
coth        coth(x)=hiperbolic cotangent of x=cosh(x)/sinh(x)
sech        sech(x)=hiperbolic secant of x=1/cosh(x)
csch        csch(x)=hiperbolic cosecant of x=1/senh(x)
asin        asin(x)=angle whose sine is x
acos        acos(x)=angle whose cosine is x
atan        atan(x)=angle whose tangent is x

There is also a random number uniformly distributed on the unit interval [0.0,1.0]:

rnd

The operators and other symbols understood by the expression analyser of Descartes are:

(   left parenthesis
)   right parenthesis
=   equal to, binary operator with a boolean result.
#   unequal to, binary operator with a boolean result.
|   or, binary boolean operator OR
&   and, binary boolean operator AND
>   greater than, binary operator with a boolean result.
<   less than, binary operator with a boolean result.
+   plus sign, binary addition operator
-   minus sign, binary subtraction operator and unary operator to change the sign
*   times, binary multiplication
/   divided by, binary division
^   binary exponontiation operator (a^b means a to the power b)
%   module, binary residue operator, the result is the residue in integer division
~   not, unary boolean operation of neagtion.

Introduction  Appetizer  Examples  Documentation  Applications  Work plan

	Ministerio de Educación, Cultura y Deporte. Aņo 2000