At present optics matrix is poorly suited to solve difficult problems of geometrical optics. The essence of the work is the use of matrix optics for analysis and construction of optical systems in the form of original matrix equations linking design features with working conditions of the optical system. Matrix equations are subjected to differentiation with respect to construction parameters. Matrix analytic functions are developed further in a finite series, because of vanishing derivatives of higher orders. In this way we obtain a methodology that is intended for analysis and construction of elaborated optical systems. Design methodology described in this work relies on carrying out certain operations to change the construction parameters starting with given roughly the optical system. These operations can be carried out in the entire optical system and its parts. The program enables calculation all partial derivatives with respect of individual and mixed construction parameters giving information if using these parameters for the correction of requirements is possible. Tables and graphs are helpful to initial design process.© (2010) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.