The guide discusses the approximation of functions by interpolation polynomials, generalized Fourier polynomials and splines. Based on interpolation, various formulas of numerical differentiation and integration are derived. One-step and multi-step methods for solving initial problems for ordinary differential equations are studied, their numerical stability is investigated; for boundary value problems, both approximate analytical and numerical methods are given. Methods of constructing solution frameworks of linear integral equations and their resolvents are shown. The presentation of the theory is accompanied by demonstrative examples, tables, figures; each chapter concludes with exercises. In the application you can find samples of laboratory tests. The proposed edition continues the author's book "Numerical Methods. Linear algebra and nonlinear equations," but can be used independently by anyone interested in computational mathematics.