Substitution and numerical evaluation
Substitution allows you to create a new mathematical expression by replacing terms
in an existing mathematical expression with new values. These values can be either
numerical values or they can be other mathematical expressions.
This process is useful for two purposes.
The first is to build up a complex expression by substituting mathematical expressions
for variables in the original expression.
The second is to plug in numbers to replace variables in a mathematical expression to
get the answer.
Either of these two purposes can be accomplished with the subs
command that takes the form
newExpression := subs(x=value1, y=value2, existingExpression)
where x and y are variables in the original expression. There can be as many variables, such as x and y as you wish. Only two were used here for simplicity.
The existing mathematical expression remains unchanged. In this way you can substitute different sets of numerical values into it many times; each time creating a new result. This is the preferred way to solve engineering problems. You first derive a mathematical expression that expresses the solution in symbolic form (i.e. expressed in terms of variable names) and then you plug in numbers to get the final numerical result.
Maple always tries to display numbers as integers or rational fractions and
not as decimal numbers. Numeric evaluation to obtain a decimal result is
accomplished with the evalf
command
evalf( expression )
The number of significant digits can be specified using [ ] immediately after evalf
and before the ( )
, for example,
evalf[6]( Pi )
will result in 3.14159 being displayed.