Analytic Geometry by V. A. Ilyin; E. G. Poznyak

This book is based on lectures delivered by the authors at the Physics Department of Moscow University.

In addition to the traditional material usually presented in the course of analytic geometry, this textbook includes some problems which find application in physics and theoretical mechanics (such as the notion of barycentric coordinates, the role of Euler’s angles in problems related to the transformation of coordinates, and the presentation of arbitrary transformations as translations and rotations in space, optical properties of second-order curves, etc.).

Also of interest is the Appendix containing Hilbert’s system of axioms, the substantiation of the method of coordinates, and the fundamentals of non-Euclidean geometry.

This textbook was awarded the 1980 State Prize of the USSR.

About the Authors

Professor I. V. Vladimir Aleksandrovich, D.Sc. (Physics and Mathematics),
Head of the Chair at Moscow University, with research work at the Institute of Mathematics of the USSR Academy of Sciences, winner of the Lomonosov Prize and the USSR State Prize. He is the author of numerous textbooks for universities and over a hundred scientific papers in the theory of partial differential equations, the theory of functions, and functional analysis, as well as in the theory of differential operators. His most important works include studies on exact conditions for elliptic operators in algebraic geometry, spectral expansions, and conditions for solvability of boundary-value and mixed problems for differential operators with non-smooth coefficients and non-smooth boundary manifolds.

Professor Poznyak Eduard Genrikhovich, D.Sc. (Physics and Mathematics),
Lecturer of Mathematics at the Physics Department of Moscow State University, winner of the USSR State Prize. He is the author of several university textbooks and more than 70 scientific papers dealing with various divisions of geometry and differential equations related to geometry. His most important results are connected with the theory of isometric embeddings in higher-dimensional Riemannian manifolds of negative curvature in Euclidean spaces, investigations related to Lobachevsky’s geometry, and various divisions of natural sciences.

Translated from the Russian by Irene Aleksanova

You can get the book here and here

Twitter https://x.com/MirTitles

Mastadon https://mastodon.social/@mirtitles

Bluesky https://bsky.app/profile/mirtitles.bsky.social

Tumblr https://www.tumblr.com/mirtitles

Internet Archive https://archive.org/details/mir-titles

Fork us on gitlab https://gitlab.com/mirtitles