Course Of Mathematical Analysis

Mathematical analysis, in the broad sense of the term, includes a very large part of mathematics. It includes differential calculus; integral calculus; the theory of functions of a real variable; the theory of functions of a complex variable; approximation theory; the theory of ordinary differential equations; the theory of partial differential equations; the theory of integral equations; differential geometry; variational calculus; functional analysis; harmonic analysis; and certain other mathematical disciplines. Modern number theory and probability theory use and develop methods of mathematical analysis. Everywhere in nature and technology one meets motions and processes which are characterized by functions; the laws of natural phenomena also are usually described by functions. Hence the objective importance of mathematical analysis as a means of studying functions. A useful book for students and professionals in the field of mathematics. In mathematical analysis the elementary functions are of fundamental importance. Basically, in practice, one operates with the elementary functions and more complicated functions are approximated by them. The elementary functions can be considered not only for real but also for complex ; then the conception of these functions becomes in some sense, complete. In this connection an important branch of mathematics has arisen, called the theory of functions of a complex variable, or the theory of analytic functions. Contents: Sequences and Series of Functions; Integration of Vectors Function; Regression Analysis; Probability-generating Function; Coordinate Systems; Theorems in Real Analysis; Functions of Real Analysis; General Relativity; Analytical Mechanics; Analytic Element Method; Topological Module; Arithmetic Progression.