General Course of Mathematics: For Beginner Math Users

The book informally sets out information on the sections of mathematics necessary for a fairly wide circle of its users: the analysis of the functions of one and several variables, linear algebra and analytical geometry, ordinary differential equations, functions of a complex variable, probability theory and mathematical statistics.
The first chapter discusses the concepts of infinitely small and infinitely large functions, 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 quite a lot to freely treat the formulas containing 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 technique of calculating certain and non -unit integrals are considered. The fourth chapter is devoted to linear spaces, their transformations, as well as 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. The sixth chapter sets out the initial information about ordinary differential equations, with an emphasis on geometric interpretation, examines the equations integrated in quadrature, and their integration technique, as well as linear equations with constant coefficients. The translation of the user in a complex plane in the seventh chapter 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 discusses the transformations of Fourier and initial information about generalized functions) In the eighth chapter, all more complicated examples present the initial concepts of probability theory and mathematical statistics.
The book is addressed to a wide range of users of mathematics, ranging from high school students, and ending with those who have long received a formal education