• Corpus ID: 119654524

Course of analytical geometry

@article{Sharipov2011CourseOA,
  title={Course of analytical geometry},
  author={Ruslan A. Sharipov},
  journal={arXiv: History and Overview},
  year={2011}
}
  • R. Sharipov
  • Published 28 November 2011
  • Physics
  • arXiv: History and Overview
This book is a regular textbook of analytical geometry covering vector algebra and its applications to describing straight lines, planes, and quadrics in two and three dimensions. The stress is made on vector algebra by using skew-angular coordinates and by introducing some notations and prerequisites for understanding tensors. The book is addressed to students specializing in mathematics, physics, engineering, and technologies and to students of other specialities where educational standards… 

Figures from this paper

On quartic forms associated with cubic transformations of the real plane

A polynomial transformation of the real plane $\Bbb R^2$ is a mapping $\Bbb R^2\to\Bbb R^2$ given by two polynomials of two variables. Such a transformation is called cubic if the degrees of its

Asymptotic estimates for roots of the cuboid characteristic equation in the linear region

A perfect cuboid is a rectangular parallelepiped. Its edges, its face diagonals, and its space diagonal are of integer lengths. None of such cuboids is known thus far, though the system of

On positive bivariate quartic forms

A bivariate quartic form is a homogeneous bivariate polynomial of degree four. A criterion of positivity for such a form is known. In the present paper this criterion is reformulated in terms of

A rough classification of potentially invertible cubic transformations of the real plane

A polynomial transformation of the real plane $\Bbb R^2$ is a mapping $\Bbb R^2\to\Bbb R^2$ given by two polynomials of two variables. Such a transformation is called cubic if the degrees of its

On cylindrical regression in three-dimensional Euclidean space

TLDR
If one replaces the root mean square averaging by a certain biquadratic averaging, the resulting problem has an almost analytic solution and is reproduced in the present paper in a coordinate-free form.

On some higher degree sign-definite multivariate polynomials associated with definite quadratic forms

Positive and negative quadratic forms are well known and widely used. They are multivariate homogeneous polynomials of degree two taking positive or negative values respectively for any values of

On linear regression in three-dimensional Euclidean space

TLDR
This problem of finding a spacial straight line best fitting a group of points in three-dimensional Euclidean space is considered and a solution to it is given in a coordinate-free form.

On simultaneous approximation of several eigenvalues of a semi-definite self-adjoint linear operator in a Hilbert space

A lower semi-definite self-adjoint linear operator in a Hilbert space is taken whose discrete spectrum is not empty and comprises at least several eigenvalues

The Diffraction of Microparticles on Single-layer and Multi-layer Statistically Uneven Surfaces

In this article: a) a method is developed for calculating volumetric diagrams of elastic scattering of microparticles (in particular, electrons and photons) on single-layer and multi-layer

Hadamard matrices in {0, 1} presentation and an algorithm for generating them

TLDR
This presentation of Hadamard matrices is investigated and based on it an algorithm for generating them is designed.