Vector and Tensor Analysis First Edition by Hay ISBN 9780486601090 0486601099
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Product details:
ISBN 10: 0486601099
ISBN 13: 9780486601090
Author: G. E. Hay
“Remarkably comprehensive, concise and clear.” — Industrial Laboratories”Considered as a condensed text in the classical manner, the book can well be recommended.” — NatureHere is a clear introduction to classic vector and tensor analysis for students of engineering and mathematical physics. Chapters range from elementary operations and applications of geometry, to application of vectors to mechanics, partial differentiation, integration, and tensor analysis. More than 200 problems are included throughout the book.
Table of contents:
CHAPTER I. ELEMENTARY OPERATIONS
1. Definitions
2. Addition of vectors
3. Multiplication of a vector by a scalar
4. Subtraction of vectors.
5. Linear functions
6. Rectangular cartesian coordinates
7. The scalar product
8. The vector product
9. Multiple products of vectors
10. Moment of a vector about a point
11. Moment of a vector about a directed line
12. Differentiation with respect to a scalar variable
13. Integration with respect to a scalar variable
14. Linear vector differential equations Problems
CHAPTER II. APPLICATIONS TO GEOMETRY
15. Introduction .
16. Some theorms of plane geometry
Solid Analytic Geometry
17. Notation
18. Division of a line segment in a given ratio
19. The distance between two points
20. The area of a triangle.
21. The equation of a plane
22. The vector-perpendicular from a point to a plane
23. The equation of a line
24. The equation of a sphere
25. The tangent plane to a sphere
Differential Geometry
26. Introduction.
27. The principal triad.
28. The Serret-Frenet formulas
29. Curvature and torsion
Problems
CHAPTER III. APPLICATION OF VECTORS TO MECHANICS
Motion of a Particle
30. Kinematics of a particle
31. Newton’s laws
32. Motion of a particle acted upon by a force which is a given function of the time.
33. Simple harmonic motion
34. Central orbits
Motion of a System of Particles
35. The center of mass of a system of particles
36. The moments and products of inertia of a system of particles
37. Kinematics of a rigid body
38. The time derivative of a vector.
39. Linear and angular momentum
40. The motion of a system of particles
41. The motion of a rigid body with a fixed point
42. The general motion of a rigid body
Problems
CHAPTER IV. PARTIAL DIFFERENTIATION
43. Scalar and vector fields
44. Directional derivatives. The operator del
45. Properties of the operator del
46. Some additional operators
47. Invariance of the operator del
48. Differentiation formulas
49. Curvilinear coordinates
50. The expressions Vf, b and b in curvilinear coordi-
nates
Problems
CHAPTER V. INTEGRATION
51. Line integrals
52. Surface integrals
53. Triple integrals
Problems
54. Green’s theorem in the plane
55. Green’s theorem in space
56. The symmetric form of Green’s theorem.
57. Stokes’s theorem
58. Integration formulas
59. Irrotational vectors
60. Solenoidal vectors
Problems
CHAPTER VI. TENSOR ANALYSIS
61. Introduction.
62. Transformation of coordinates
63. Contravariant vectors and tensors
64. Covariant vectors and tensors
65. Mixed tensors. Invariants
66. Addition and multiplication of tensors
67. Some properties of tensors
68. Tests for tensor character
69. The metric tensor
70. The conjugate tensor
71. Lowering and raising of suffixes
72. Magnitude of a vector. Angle between two vectors
73. Geodesics
74. Transformation of the Christoffel symbols
75. Absolute differentiation
76. Covariant derivatives
77. The curvature tensor
78. Cartesian tensors
79. Oriented cartesian tensors
80. Relative tensors
81. Physical components of tensors
82. Applications
Problems
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