Course of Analytical Geometry by Ruslan Sharipov - Free PDF

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About this book :-
This is a regular textbook of analytical geometry for students studying math, physics, or engineering. It is covering vector algebra and its applications to describing straight lines, planes, and quadrics in two and three dimensions. The book explains complex ideas in a way that is both careful and easy to follow, making it a great starting point for deeper studies in geometry and related areas.

Book Detail :-
This book has following details information.
Title: Course of Analytical Geometry by Ruslan Sharipov - Free PDF
Publisher: UFA
Year: 2011
Pages: 227
Type: PDF
Language: English
ISBN-10 #: N\A
ISBN-13 #: N\A
License: N\A
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About Author :-
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Book Contents :-
This book has following table of contents.
Part-I VECTOR ALGEBRA 1. Three-dimensional Euclidean space. Acsiomatics and visual evidence 2. Geometric vectors. Vectors bound to points 3. Equality of vectors 4. The concept of a free vector 5. Vector addition 6. Multiplication of a vector by a number 7. Properties of the algebraic operations with vectors 8. Vectorial expressions and their transformations 9. Linear combinations. Triviality, non-triviality, and vanishing 10. Linear dependence and linear independence 11. Properties of the linear dependence 12. Linear dependence for n = 1 13. Linear dependence for n = 2. Collinearity of vectors 14. Linear dependence for n = 3. Coplanartity of vectors 15. Linear dependence for n > 4 16. Bases on a line 17. Bases on a plane 18. Bases in the space 19. Uniqueness of the expansion of a vector in a basis 20. Index setting convention 21. Usage of the coordinates of vectors 22. Changing a basis. Transition formulas and transition matrices 23. Some information on transition matrices 24. Index setting in sums 25. Transformation of the coordinates of vectors under a change of a basis 26. Scalar product 27. Orthogonal projection onto a line 28. Properties of the scalar product 29. Calculation of the scalar product through the coordinates of vectors in a skew-angular basis 30. Symmetry of the Gram matrix 31. Orthonormal basis 32. The Gram matrix of an orthonormal basis 33. Calculation of the scalar product through the coordinates of vectors in an orthonormal basis 34. Right and left triples of vectors. The concept of orientation 35. Vector product 36. Orthogonal projection onto a plane 37. Rotation about an axis 38. The relation of the vector product with projections and rotations 39. Properties of the vector product 40. Structural constants of the vector product 41. Calculation of the vector product through the coordinates of vectors in a skew-angular basis 42. Structural constants of the vector product in an orthonormal basis 43. Levi-Civita symbol 44. Calculation of the vector product through the coordinates of vectors in an orthonormal basis 45. Mixed product 46. Calculation of the mixed product through the coordinates of vectors in an orthonormal basis 47. Properties of the mixed product 48. The concept of the oriented volume 49. Structural constants of the mixed product 50. Calculation of the mixed product through the coordinates of vectors in a skew-angular basis 51. The relation of structural constants of the vectorial and mixed products 52. Effectivization of the formulas for calculating vectorial and mixed products 53. Orientation of the space 54. Contraction formulas 55. The triple product expansion formula and the Jacobi identity 56. The product of two mixed products Part-II GEOMETRY OF LINES AND SURFACES 1. Cartesian coordinate systems 2. Equations of lines and surfaces 3. A straight line on a plane 4. A plane in the space 5. A straight line in the space 6. Ellipse. Canonical equation of an ellipse 7. The eccentricity and directrices of an ellipse. The property of directrices 8. The equation of a tangent line to an ellipse 9. Focal property of an ellipse 10. Hyperbola. Canonical equation of a hyperbola 11. The eccentricity and directrices of a hyperbola. The property of directrices 12. The equation of a tangent line to a hyperbola. 13. Focal property of a hyperbola. 14. Asymptotes of a hyperbola 15. Parabola. Canonical equation of a parabola 16. The eccentricity of a parabola 17. The equation of a tangent line to a parabola 18. Focal property of a parabola 19. The scale of eccentricities 20. Changing a coordinate system 21. Transformation of the coordinates of a point under a change of a coordinate system 22. Rotation of a rectangular coordinate system on a plane. The rotation matrix 23. Curves of the second order 24. Classification of curves of the second order 25. Surfaces of the second order 26. Classification of surfaces of the second order

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