Normal view MARC view ISBD view

A brief course in analytic geometry / N. Yefimov ; translated from the Russian by O. Soroka.

By: Efimov, N. V. (Nikolai Vladimirovich), 1910-.
Material type: materialTypeLabelBookPublisher: Moscow : Peace Publishers, [1964]Description: 251 p. : il. ; 23 cm.Uniform titles: Kratkii kurs analiticheskoi geometrii. Inglés Subject(s): Geometry, AnalyticOther classification: 51-01 (51N20)
Contents:
Part One -- PLANE ANALYTIC GEOMETRY -- Chapter 1. Coordinates on a Straight Line and in a Plane [11] -- § 1. An Axis and Segments of an Axis [11] -- § 2. Coordinates on a Line. The Number Axis [14] -- § 3. Rectangular Cartesian Coordinates in a Plane. A Note on Oblique Cartesian Coordinates [16] -- § 4. Polar Coordinates [20] -- Chapter 2. Elementary Problems of Plane Analytic Geometry [23] -- § 5. Projection of a Line Segment. Distance Between Two Points [23] -- § 6. Calculation of the Area of a Triangle [28] -- § 7. Division of a Line Segment in a Given Ratio [30] -- § 8. Transformation of Cartesian Coordinates by .Translation of Axes [35] -- § 9. Transformation of Rectangular Cartesian Coordinates by Rotation of Axes [36] -- § 10. Transformation of Rectangular Cartesian Coordinates by Change of Origin and Rotation of Axes [38] -- Chapter 3. The Equation of a Curve [41] -- § 11. The Concept of the Equation of a Curve. Examples of Curves Represented by Equations [41] -- § 12. Examples of Deriving the Equation of a Given Curve [48] -- § 13. The Problem of the Intersection of Two Curves [50] -- § 14. Parametric Equations of a Curve [51] -- § 15. Algebraic Curves [52] -- Chapter 4. Curves of the First Order [55] -- § 16. The Slope of a Straight Line [55] -- § 17. The Slope-intercept Equation of a Straight Line [56] -- § 18. Calculation of the Angle Between Two Straight Lines. Conditions for the Parallelism and Perpendicularity of Two Straight Lines [59] -- § 19. The Straight Line As the Curve of the First Order. The General Equation of the Straight Line [61] -- § 20. Incomplete Equations of the First Degree. The Intercept Equation of a Straight Line [63] -- § 21. Discussion of a System of Equations Representing Two Straight Lines [65] -- § 22. The Normal Equation of a Straight Line. The Problem of Calculating the Distance of a Point from a Straight Line [68] -- § 23. The Equation of a Pencil of Lines [71] -- Chapter 5. Geometric Properties of Curves of the Second Order [75] -- § 24. The Ellipse. Definition of the Ellipse and Derivation of Its Canonical Equation [75] -- § 25. Discussion of the Shape of the Ellipse [79] -- § 26. The Eccentricity of the Ellipse [81] -- § 27. Rational Expressions for Focal Radii of the Ellipse [82] -- § 28. Point-by-point Construction of the Ellipse. The Parametric Equations of the Ellipse [83] -- § 29. The Ellipse as the Projection of a Circle on a Plane. The Ellipse as the Section of a Circular Cylinder by a Plane [84] -- § 30. The Hyperbola. Definition of the Hyperbola and Derivation of Its Canonical Equation [87] -- § 31. Discussion of the Shape of the Hyperbola [91] -- § 32. The Eccentricity of the Hyperbola [97] -- § 33. Rational Expressions for Focal Radii of the Hyperbola [98] -- § 34. The Directrices of the Ellipse and Hyperbola [99] -- § 35. The Parabola. Derivation of the Canonical Equation of the Parabola [103] -- § 36. Discussion of the Shape of the Parabola [105] -- § 37. The Polar Equation of the Ellipse, Hyperbola and Parabola [107] -- § 38. Diameters of Curves of the Second Order [109] -- § 39. The Optical Properties of the Ellipse, Hyperbola and Parabola [114] -- § 40. The Ellipse, Hyperbola and Parabola as Conic Sections [115] -- Chapter 6. Transformation of Equations by Change of Coordinates [116] -- § 41. Examples of Reducing the General Equation of a Second-Order Curve to Canonical Form [116] -- § 42. The Hyperbola as the Inverse Proportionality Graph. The Parabola as the Graph of a Quadratic Function [125] -- Part Two -- SOLID ANALYTIC GEOMETRY -- Chapter 7. Some Elementary Problems of Solid Analytic Geometry [131] -- § 43. Rectangular Cartesian Coordinates in Space [131] -- € 44 The Concept of a Free Vector. The Projection of a Vector on an Axis [134] -- § 45. The Projections of a Vector on the Coordinate Axes [138] -- § 46. Direction Cosines [141] -- § 47. Distance between Two Points. Division of a Line Segment in a Given Ratio [142] -- Chapter & Linear Operations on Vectors [143] -- § 48. Definitions of Linear Operations [143] -- § 49. Basic Properties of Linear Operations [144] -- § 50. The Vector Difference [147] -- § 51. Fundamental Theorems on Projections [149] -- § 52. Resolution of Vectors into Components [152] -- Chapter 9. The Scalar Product of Vectors [157] -- § 53. The Scalar Product and Its Basic Properties [157] -- § 54. Representation of the Scalar Product in Terms of the Coordinates of the Vector Factors [160] -- Chapter 10. The Vector and Triple Scalar Products of Vectors [163] -- § 55. The Vector Product and Its Basic Properties [163] -- § 56. Representation of the Vector Product in Terms of the Coordinates of the Vector Factors [170] -- § 57. The Triple Scalar Product [172] -- § 58. Representation of the Triple Scalar Product in Terms of the Coordinates of the Vector Factors [176] -- Chapter 11. The Equation of a Surface and the Equations of a Curve [178] -- § 59. The Equation of a Surface [178] -- § 60. The Equations of a Curve. The Problem of the Intersection of Three Surfaces [179] -- § 61. The Equation of a Cylindrical Surface with Elements Parallel to a Coordinate Axis [181] -- § 62. Algebraic Surfaces [183] -- Chapter 12. The Plane as the Surface of the First Order. The Equations of a Straight Line [185] -- § 63. The Plane as the Surface of the First Order [185] -- § 64. Incomplete Equations of Planes. The Intercept Form of the Equation of a Plane [188] -- § 65. The Normal Equation of a Plane. The Distance of a Point from a Plane [190] -- § 66. The Equations of a Straight Line [194] -- § 67. The Direction Vector of a Straight Line. The Canonical Equations of a Straight Line. The Parametric Equations of a Straight Line [198] -- § 68. Some Additional Propositions and Examples [201] -- Chapter 13. Quadric Surfaces [207] -- § 69. The Ellipsoid and the Hyperboloids [207] -- § 70. The Quadric Cone [213] -- § 71 The Paraboloids [215] -- § 72. The Quadric Cylinders [219] -- § 73. The Rectilinear Generators of the Hyperboloid of One Sheet. The Shukhov Towers [220] -- Appendix. The Elements of the Theory of Determinants [225] -- § 1. Determinants of the Second Order and Systems of Two Equations of the First Degree in Two Unknowns [225] -- § 2. A Homogeneous System of Two Equations of the First Degree in Three Unknowns [229] -- § 3. Determinants of the Third Order [232] -- § 4. Cofactors and Minors [236] -- § 5. Solution and Analysis of a System of Three First-degree Equations in Three Unknowns [240] -- § 6, The Concept of a Determinant of Any Order [247] --
List(s) this item appears in: ÚLTIMOS LIBROS INCORPORADOS
Tags from this library: No tags from this library for this title. Log in to add tags.
    average rating: 0.0 (0 votes)
Item type Home library Shelving location Call number Status Date due Barcode Course reserves
Libros Libros Instituto de Matemática, CONICET-UNS
Últimas adquisiciones 51 Ef27 (Browse shelf) Available A-9227

INTRODUCCIÓN A LA MATEMÁTICA

MATEMÁTICA GENERAL

NOCIONES DE GEOMETRÍA ANALÍTICA


Traducción de: Kratkii kurs analiticheskoi geometrii.

Part One --
PLANE ANALYTIC GEOMETRY --
Chapter 1. Coordinates on a Straight Line and in a Plane [11] --
§ 1. An Axis and Segments of an Axis [11] --
§ 2. Coordinates on a Line. The Number Axis [14] --
§ 3. Rectangular Cartesian Coordinates in a Plane. A Note on Oblique Cartesian Coordinates [16] --
§ 4. Polar Coordinates [20] --
Chapter 2. Elementary Problems of Plane Analytic Geometry [23] --
§ 5. Projection of a Line Segment. Distance Between Two Points [23] --
§ 6. Calculation of the Area of a Triangle [28] --
§ 7. Division of a Line Segment in a Given Ratio [30] --
§ 8. Transformation of Cartesian Coordinates by .Translation of Axes [35] --
§ 9. Transformation of Rectangular Cartesian Coordinates by Rotation of Axes [36] --
§ 10. Transformation of Rectangular Cartesian Coordinates by Change of Origin and Rotation of Axes [38] --
Chapter 3. The Equation of a Curve [41] --
§ 11. The Concept of the Equation of a Curve. Examples of Curves Represented by Equations [41] --
§ 12. Examples of Deriving the Equation of a Given Curve [48] --
§ 13. The Problem of the Intersection of Two Curves [50] --
§ 14. Parametric Equations of a Curve [51] --
§ 15. Algebraic Curves [52] --
Chapter 4. Curves of the First Order [55] --
§ 16. The Slope of a Straight Line [55] --
§ 17. The Slope-intercept Equation of a Straight Line [56] --
§ 18. Calculation of the Angle Between Two Straight Lines. Conditions for the Parallelism and Perpendicularity of Two Straight Lines [59] --
§ 19. The Straight Line As the Curve of the First Order. The General Equation of the Straight Line [61] --
§ 20. Incomplete Equations of the First Degree. The Intercept Equation of a Straight Line [63] --
§ 21. Discussion of a System of Equations Representing Two Straight Lines [65] --
§ 22. The Normal Equation of a Straight Line. The Problem of Calculating the Distance of a Point from a Straight Line [68] --
§ 23. The Equation of a Pencil of Lines [71] --
Chapter 5. Geometric Properties of Curves of the Second Order [75] --
§ 24. The Ellipse. Definition of the Ellipse and Derivation of Its Canonical Equation [75] --
§ 25. Discussion of the Shape of the Ellipse [79] --
§ 26. The Eccentricity of the Ellipse [81] --
§ 27. Rational Expressions for Focal Radii of the Ellipse [82] --
§ 28. Point-by-point Construction of the Ellipse. The Parametric Equations of the Ellipse [83] --
§ 29. The Ellipse as the Projection of a Circle on a Plane. The Ellipse as the Section of a Circular Cylinder by a Plane [84] --
§ 30. The Hyperbola. Definition of the Hyperbola and Derivation of Its Canonical Equation [87] --
§ 31. Discussion of the Shape of the Hyperbola [91] --
§ 32. The Eccentricity of the Hyperbola [97] --
§ 33. Rational Expressions for Focal Radii of the Hyperbola [98] --
§ 34. The Directrices of the Ellipse and Hyperbola [99] --
§ 35. The Parabola. Derivation of the Canonical Equation of the Parabola [103] --
§ 36. Discussion of the Shape of the Parabola [105] --
§ 37. The Polar Equation of the Ellipse, Hyperbola and Parabola [107] --
§ 38. Diameters of Curves of the Second Order [109] --
§ 39. The Optical Properties of the Ellipse, Hyperbola and Parabola [114] --
§ 40. The Ellipse, Hyperbola and Parabola as Conic Sections [115] --
Chapter 6. Transformation of Equations by Change of Coordinates [116] --
§ 41. Examples of Reducing the General Equation of a Second-Order Curve to Canonical Form [116] --
§ 42. The Hyperbola as the Inverse Proportionality Graph. The Parabola as the Graph of a Quadratic Function [125] --
Part Two --
SOLID ANALYTIC GEOMETRY --
Chapter 7. Some Elementary Problems of Solid Analytic Geometry [131] --
§ 43. Rectangular Cartesian Coordinates in Space [131] --
€ 44 The Concept of a Free Vector. The Projection of a Vector on an Axis [134] --
§ 45. The Projections of a Vector on the Coordinate Axes [138] --
§ 46. Direction Cosines [141] --
§ 47. Distance between Two Points. Division of a Line Segment in a Given Ratio [142] --
Chapter & Linear Operations on Vectors [143] --
§ 48. Definitions of Linear Operations [143] --
§ 49. Basic Properties of Linear Operations [144] --
§ 50. The Vector Difference [147] --
§ 51. Fundamental Theorems on Projections [149] --
§ 52. Resolution of Vectors into Components [152] --
Chapter 9. The Scalar Product of Vectors [157] --
§ 53. The Scalar Product and Its Basic Properties [157] --
§ 54. Representation of the Scalar Product in Terms of the Coordinates of the Vector Factors [160] --
Chapter 10. The Vector and Triple Scalar Products of Vectors [163] --
§ 55. The Vector Product and Its Basic Properties [163] --
§ 56. Representation of the Vector Product in Terms of the Coordinates of the Vector Factors [170] --
§ 57. The Triple Scalar Product [172] --
§ 58. Representation of the Triple Scalar Product in Terms of the Coordinates of the Vector Factors [176] --
Chapter 11. The Equation of a Surface and the Equations of a Curve [178] --
§ 59. The Equation of a Surface [178] --
§ 60. The Equations of a Curve. The Problem of the Intersection of Three Surfaces [179] --
§ 61. The Equation of a Cylindrical Surface with Elements Parallel to a Coordinate Axis [181] --
§ 62. Algebraic Surfaces [183] --
Chapter 12. The Plane as the Surface of the First Order. The Equations of a Straight Line [185] --
§ 63. The Plane as the Surface of the First Order [185] --
§ 64. Incomplete Equations of Planes. The Intercept Form of the Equation of a Plane [188] --
§ 65. The Normal Equation of a Plane. The Distance of a Point from a Plane [190] --
§ 66. The Equations of a Straight Line [194] --
§ 67. The Direction Vector of a Straight Line. The Canonical Equations of a Straight Line. The Parametric Equations of a Straight Line [198] --
§ 68. Some Additional Propositions and Examples [201] --
Chapter 13. Quadric Surfaces [207] --
§ 69. The Ellipsoid and the Hyperboloids [207] --
§ 70. The Quadric Cone [213] --
§ 71 The Paraboloids [215] --
§ 72. The Quadric Cylinders [219] --
§ 73. The Rectilinear Generators of the Hyperboloid of One Sheet. The Shukhov Towers [220] --
Appendix. The Elements of the Theory of Determinants [225] --
§ 1. Determinants of the Second Order and Systems of Two Equations of the First Degree in Two Unknowns [225] --
§ 2. A Homogeneous System of Two Equations of the First Degree in Three Unknowns [229] --
§ 3. Determinants of the Third Order [232] --
§ 4. Cofactors and Minors [236] --
§ 5. Solution and Analysis of a System of Three First-degree Equations in Three Unknowns [240] --
§ 6, The Concept of a Determinant of Any Order [247] --

MR, REVIEW #

There are no comments for this item.

Log in to your account to post a comment.

Click on an image to view it in the image viewer

¿Necesita ayuda?

Si necesita ayuda para encontrar información, puede visitar personalmente la biblioteca en Av. Alem 1253 Bahía Blanca, llamarnos por teléfono al 291 459 5116, o enviarnos un mensaje a bibima@criba.edu.ar.
Para solicitar copias de artículos, complete el formulario o escríbanos a pedidos.inmabb@gmail.com

Powered by Koha