The notion of a qualified function is introduced as a general means of representing the parameters of dynamic systems. Two specific types of qualified functions are defined for the analysis of the behavior and performance of structured programs. Transformation functions represent the values of variables during execution and timing algorithms express the execution times of programs symbolically. Complete rules of derivation for transformation functions and timing algorithms are given for the control mechanisms of sequence, selection, fixed loop, and while statement. Deterministic and stochastic simplification of transformation functions and timing algorithms are investigated and methods of eliminating recursion for expressions corresponding to while statements are studied.