Numerical methods. Mathematical analysis and ordinary differential equations. Grif MO RF

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manual deals with the approximation of functions by interpolating polynomials, generalized Fourier polynomials and splines. Based on the interpolation output different formulas for numerical differentiation and integration. We study the one-step and multi-step methods for solving initial value problems for ordinary differential equations, we studied their numerical stability; for boundary value problems are given as approximate analytical and numerical methods actually. Shows a method of constructing skeletons of solutions of linear integral equations and their resolutions. Exposition of the theory is accompanied by demos and examples, tables, figures; each chapter ends exercises. Attached you can find samples of laboratory tasks productions. The proposed publication continues the author of the book Numerical methods (linear algebra and nonlinear equations) .- M .: ONYX 21 , 2004, but can be used independently from it all who is interested in computational mathematics.