Foundations of higher mathematics. Part 1. Linear algebra and analytic geometry
Вантажиться...
Файли
Дата
2017
Науковий керівник
Укладач
Редактор
Назва журналу
ISSN
E-ISSN
Назва тому
Видавець
Одеський національний університет імені І. І. Мечникова
Анотація
The modern level of development of a science results in that more
and more specialties which had before the applied (technical) character are
included in sphere of university education. First of all to such specialties
we should refer specialties in the field of computer sciences. Features of
training of students on these specialties at university generate a need of the
accelerated studying of a course of higher mathematics, which has the
volume coming nearer to the university course. Such challenge is issued by
this text-book on higher mathematics issues which is intended for students
of the universities specializing in the field of computer sciences. Here the
reader will find many perfectly developed pages as the course of the
general mathematics cannot be original work. The reason of it that a
course carries out the first contact to new knowledge and it is intended for
the persons finished the school education and having only principles of
elementary mathematics knowledge. Feature of the given text-book is also
the uniform methodical approach to a statement of the entire higher
mathematics course, consisting that the basic mathematical concepts
follow from the general concepts and from logic concepts with the
following distribution of a material.
The course is divided into five books.
The book 1 contains some logic concepts, the elementary concepts
concerning to sets and operations on them (union, intersection, difference,
product), and also the basic mathematical concepts, namely: concept of
function or mapping; concept of n – dimensional arithmetic space.
The book 2 is dedicated to the linear algebra. From fundamental
concept of mapping, concepts of internal and external laws of a
composition are introduced. Conditions at which operations of these laws
on a set transform them into groups, rings, fields and vector spaces are
considered. It is investigated: a field of complex numbers; a ring of
multinomials; vector space of multinomials; vector space of free vectors in
geometrical space; vectors in n – dimension arithmetic space. Concepts of
matrixes, determinants and system of the linear equations result from
concepts of vector space and linear mapping of one vector space to another
one. In the separate chapter it is considered reduction of matrixes by changing of basis to more simple form. Rather in detail, it is shown for
reduction of the square matrix to the diagonal type, and the square-law
form to the canonic type.
The book 3 contains a number of concepts of analytical geometry
required by the program: the equations of a straight line on the plane and
in the space; the equations of a plane; curves and surfaces of the second
order, the equation of curves and surfaces of the second order are reduced
to the canonical type with use of square-law forms. These geometrical
concepts act as the direct appendix of the book 2 or as transferring of
results of this book on language of geometry as it is made in it for free
vectors in geometrical space.
The book 4 is dedicated to the mathematical analysis. Numerical
functions of one and many real variables are considered. Concepts of limit
and continuity are introduced for these functions. The book comes to an
end with the statement of differential and integral calculus.
In the book 5 the chapters are collected which are concerning to the
concepts, having technical character at a level of the general mathematics
course; these are differential equations and lines.
The statement of a theoretical material is accompanied by the
illustrative examples and the solutions of typical problems. With the
purpose of reinforcement of educational material, here the exercises for
independent work are offered.
Опис
Ключові слова
general concepts, function, mapping, arithmetic space Rn, linear algebra, complex numbers, multinomials, vector spaces, matrixes, linear equation systems, matrix reduction, analytical geometry, straight line on the plane, straight line and plane in the three-dimensional space, lines and surfaces of the second order
Бібліографічний опис
Tyurin A. Foundations of higher mathematics. Part 1. Linear algebra and analytic geometry: Textbook / A. V. Tyirin, A.Yu. Akhmerov – Odessa : Odessa National Unsversity after I. I. Mechnikov, 2017. – 257 p.