# Typing Equations

DynaSys allows you to type in equations easily. It uses a standard syntax that you may already be familiar with, from programs such as Matlab or Mathematica. There are three kinds of objects on which algebraic operations may take place, listed below.

Variables are objects that take on different values at different stages of a computation. The independent variable is always called ' t '. Other variables may take any name except that of an intrinsic function (such as 'cos').

Parameters are objects that have fixed values over a given computation. You may change parameter values manually, but the program will never change them for you. Again, parameters may take any name except that of an intrinsic function.

Constants are simply numbers that you type in to the equation box. You may change them at any time by using the Edit menu, and the Equation item within it. Indeed, when dealing with a system that involves a lot of parameters, it is frequently convenient simply to type the values of most of the parameters into the equations, and then modify them as necessary.

In addition to the variables and so on, there are two types of functions that may be used.

User defined functions are essentially variables that depend on other variables. Note in particular that, while a so-called dependent variable ultimately depends only on t, a user defined function may depend on t and some dependent variables.

Intrinsic functions are simply those common mathematical functions that are necessary if one wants to solve most any differential equations. DynaSys recognizes the following intrinsic functions:

• sin(x)
• cos(x)
• tan(x)
• exp(x)
• log(x) or ln(x)
• arcsin(x) or asin(x)
• arccos(x) or acos(x)
• arctan(x) or atan(x)
• sqrt(x)
• abs(x)
• cosh(x)
• sinh(x)
• tanh(x)
• sign(x) or sgn(x)
• heaviside(x)

Kevin Cooper
Wed Sep 30 15:21:52 PDT 1998