Differential calculus made easy

A distinctive feature of the proposed manual is close union of the ideas of linear algebra and differential calculus, which makes it possible to achieve a great generality of presentation, taking as the initial mapping R n → R m , considering the mapping
R → R, R n → R and R → R n as special cases. The manual consists of five chapters. The first chapter covers the basic concepts mathematical analysis limit and continuity after prevariable definition of a system of neighborhoods of points on a straight line, plane and in space.
The second chapter presents the differential calculus for functions of one and many variables. As initial the concepts of differentiable mapping, differentiable la and the derivative of the matrix. The structure of the derivative in the most important cases for the application. In the same chapter included traditional material of research of functions.
The third and fourth chapters contain guidelines, in which the methods of solving typical problems by mathematic analysis to assist students in performing the control works given in the fifth chapter. Provide ren the possibility of automated self-control if available device "Symbol" or its computer equivalent, developed by at Tomsk State University of control systems and radio electronics.
The manual is intended for students of technical and economic specialties of correspondence and distance learning.
1. Introduction to mathematical analysis
1.1. Sets. Set operations