1550078481-Ordinary_Differential_Equations__Roberts_

510 Ordinary Differential Equations

Table A.2 Additional Mathematical Functions

Functions Computation in BASIC Comments

Arccos x 2.0*atn(x) - atn(x/sqr(l.O - x*x)) Arccosine function

-1<x< 1

Arcsin x atn(x/sqr(l.O - X*x)) Arcsine function

-1<x<1

coshx (exp(x) +exp( - x))/ 2.0 Hyperbolic cosine

function

cotx 1.0/tan(x) Cotangent function

x must be in radians

cscx 1.0/sin(x) Cosecant function

x must be in radians

logax log(x)/ log(a) Logarithm function

base a where x > 0 ,

a > 0, and a i= l.

Common logarithm

when a= 10.

secx 1.0/cos(x) Secant function

x must be in radians

sinhx ( exp(x) - exp( - x)) /2.0 Hyperbolic sine

function

tanhx 1.0 - 2.0*exp( - x)/(exp(x)+exp( - x)) Hyperbolic tangent

function

Using GRAPH

The program GRAPH will graph a function y = f(x) in a rectangular
region R of the xy-plane bounded by the lines x = Xmin, x = Xmax,
y = Y min, and y = Y max. The region R is sometimes called a "window"
because graphing y = f(x) in R is like looking at a portion of the xy-plane
through a rectangular picture window. You specify the function f(x) to be