The monograph is devoted to the illustration of the capabilities of one of the most effective computer mathematics systems MATLAB in solving a number of scientific and engineering problems. Examples of solving problems of mathematical analysis. are considered. Classical numerical methods are supplemented by examples of more complex engineering and scientific problems of mathematical physics. Algorithms of boundary problems of statics, dynamics and stability of elastic systems in the method of boundary elements are described in detail . MATLAB system extensions of symbolic calculations, optimization and modeling are considered. The use of computer technologies to solve problems through the MATLAB system is illustrated by a large number of exercises and examples. Designed for students and postgraduates of higher technical educational institutions, it will be useful for specialists and researchers of a wide profile.