In the textbook, sections of the solution of nonlinear algebraic equations and systems, ordinary differential equations and equations in first-order partial derivatives are considered. Examples of problem solving and options for tasks for self-fulfillment within the framework of the standard program of the course "Numbered methods" are given. The textbook contains the basic definitions and the necessary theorems to the extent sufficient for their successful application in the performance of independent works. Designed for students of the Faculty of Mechanics and Mathematics of the UNN, studying in the areas of training 010100 "Mathematics", 010200 "Mathematics and Computer Science", 010400 "Applied Mathematics and Informatics" .