The general course of mathematics. Alekseev D.V.

The book informally sets out information on the sections of mathematics, the necessary fairly wide circle of its users:

• to the analysis of the functions of one and several variables;
• linear algebra and analytical geometry; /li>
• ordinary differential equations;
• functions of a complex variable;
• the theory of probability and mathematical statistics.

The first chapter examines the concept infinitely small and infinitely large functions, a derivative, the first -shaped, a certain integral, the steppe series.

The second chapter is an analogue of the “Multiplication Table”, supplying the user with the initial margin of specific functions, which he should know, if not everything, then, then, then not everything, then There are quite a lot to freely handle these functions.

the first sections of the third chapter are devoted to the “elementary” technique of differentiation and integration that each user of mathematics should own, further integrals and the calculation technique of certain and non -universal Integles.

The fourth chapter is devoted to linear spaces, their transformations, as well as the fifth chapter necessary for the further “geometric minimum.” The fifth chapter contains basic information related to the functions of several variables:

• differentiation;
• extremums (including conditional);
• double, triple, curved and surface integrals;
• differentiation and integration of vector fields.

In the sixth chapter, the initial information about ordinary differential equations, with an emphasis on geometric interpretation, is considered, the equations integrated in the quadrature, and their integration technique of replacement of variables, as well as linear equations with constant coefficients.

The translation of the user into a complex plane in the seventh chapter in significantly expands its capabilities, both in the technique of calculating integrals and solving differential equations, and in the ability to grasp new structures (therefore, it also considers the transformations of Fourier and initial information about generalized functions).

In the eighth chapter, all more complicated examples set out initial pronounces of probability theory and mathematical statistics.

The book is addressed to a wide circle of mathematics users, starting from high school students, and Finishing those who have long received a “formal” education.