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

##### By: Efimov, N. V. (Nikolai Vladimirovich).

Material type: BookPublisher: 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)Item type | Home library | Shelving location | Call number | Status | Date due | Barcode | Course reserves |
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Libros | Instituto de Matemática, CONICET-UNS | Últimas adquisiciones | 51 Ef27 (Browse shelf) | Available | A-9227 |

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 #

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