This manual serves as a guide for students to independently complete tasks and is compiled in accordance with the programs: "Computational Mathematics," "Informatics," "Modeling Systems and Processes," "Informatics and Information Technologies," can be useful for students of engineering specialties and directions. The manual contains brief theoretical material on the topics: "Numerical integration," "Numerical solution of differential equations and systems," "Method of grids for solving the wave equation," "Solving hard problems," "Overview of mathematical software systems." The tutorial provides recommendations for using Mathcad (Professional-2000) and provides detailed solutions to problems on these topics with detailed explanations and with Python solution algorithms.