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.