Pogorelov - Analytical Geometry torrent

Analytical Geometry by A. V. Pogorelov.

Analytical geometry has no strictly defined contents. It is the
method but not the subject under investigation, that constitutes the
leading feature of this branch of geometry.

The essence of this method consists in that geometric objects are
associated in some standard way with equations (or systems of
equations) so that geometric relations of figures are expressed
through properties of their equations.

For instance, in case of Cartesian coordinates any straight line in
the plane is uniquely associated with a linear equation ax+by+ c =
0.

The intersection of three straight, lines at one point is
expressed by the condition of compatibility of a system of three
equations which specify these lines.

Due to a multipurpose approach to solving various problems, the
method of analytic geometry has become the leading method in
geometric investigations and is widely applied in other fields of
exact natural sciences, such as mechanics and physics.

Analytical geometry joined geometry with algebra and analysis -
the fact which has told fruitfully on further development of
these three subject of mathematics.

The principal ideas of analytical geometry are traced back to the
French mathematician, Rene Descartes (1595-1650), who in 1637
described the fundamentals of its method in his famous work
"Geometric".
What this book is about and whom it is for?

The present book, which is a course of lectures, treats the
fundamentals of the method of analytic geometry as applied to the
simplest geometric objects. It is designed for the university
students majoring in physics and mathematics,


This book was translated from the Russian by Leonid Levant and
was first published by Mir Publishers in 1980.

All credits to the original uploader.

DJVU | 3.1 MB | Pages: 239 |

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Table of Contents

Chapter 1
Rectangular Cartesian Coordinates In a Plane 11

Chapter 2
The Straight Line 32

Chapter 3
Conic Sections 55

Chapter 4
Vectors 87

Chapter 5
Rectangular Cartesian Coordinates in Space 106

Chapter 6
A Plane and a Straight Line 119

Chapter 7
Surfaces of the Second Order (Quadric Surfaces)

Chapter 8
Investigating Quadric Curves and Surfaces Specified by Equations of
the General Form 160

Chapter 9
Linear Transformations 180

Answers to the Exercises, Hints and Solutions 211