A variable usually gets its value through an assignment statement. If it is a formal parameter in a function definition, it gets its value when the function is called. (There is an implicit assignment, as we have noted above.) Subsequent references to the variable recall the assigned value. The region of code in which a variable's assigned values are accessible is called the variable's ``scope''. When a variable is referenced outside of its scope, Python complains that it is undefined.
The scope is defined in terms of code ``blocks''. In the example above, the function bodies are code blocks. The entire code is also a code block.
A variable's scope extends only to the end of the smallest code block
in which its value is assigned. In the above example, the variable
N is assigned at the top of the code, so its value is
accessible throughout the entire code from there on. Its scope is
said to be ``global''. The variable
pnew, on the other
hand, is defined only inside the
main() function. So its
scope is limited (``local'') to the
main() function block.
x is defined in the function
so its scope is local to that function. In the
example above, the variables
local to that function.
A consequence of variable scoping rules is that the values assigned to
dydx in the function
f_and_df cannot be accessed with those names in the
main() function. That is, if you tried to do