Chapter: Derivatives of Tensors, Covariant Derivatives

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Home > A Primer in Tensor Analysis and Relativity > Derivatives of Tensors, Covariant Derivatives

A Primer in Tensor Analysis and Relativity |

Ilya L. Shapiro

Springer International Publishing

A Primer in Tensor Analysis and Relativity

Derivatives of Tensors, Covariant Derivatives

Chapter Info

Authors

Ilya L. Shapiro

ARI Id

1665210425425_5376378

Access

Not Available Free

Pages

55-65

DOI

10.1007/978-3-030-26895-4_5

Chapter URL

https://rd.springer.com/chapter/10.1007/978-3-030-26895-4_5

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Chapters/Headings	Author(s)	Pages	Info
Front Matter		i-xviii
Front Matter		1-1
Linear Spaces, Vectors, and Tensors	Ilya L. Shapiro	3-20
Operations over Tensors, Metric Tensor	Ilya L. Shapiro	21-26
Symmetric, Skew(Anti) Symmetric Tensors, and Determinants	Ilya L. Shapiro	27-44
Curvilinear Coordinates, Local Coordinate Transformations	Ilya L. Shapiro	45-54
Derivatives of Tensors, Covariant Derivatives	Ilya L. Shapiro	55-65
Grad, div, rot, and Relations Between Them	Ilya L. Shapiro	67-70
Grad, div, rot, and \(\Delta \) in Cylindric and Spherical Coordinates	Ilya L. Shapiro	71-80
Curvilinear, Surface, and D-Dimensional Integrals	Ilya L. Shapiro	81-99
Theorems of Green, Stokes, and Gauss	Ilya L. Shapiro	101-108
Solutions to the Exercises from Part 1	Ilya L. Shapiro	109-127
Front Matter		129-129
Maxwell Equations and Lorentz Transformations	Ilya L. Shapiro	131-142
Laws of Relativistic Mechanics	Ilya L. Shapiro	143-158
Maxwell Equations in Relativistic Form	Ilya L. Shapiro	159-187
Front Matter		189-190
Equivalence Principle, Covariance, and Curvature Tensor	Ilya L. Shapiro	191-223
Einstein Equations, Schwarzschild Solution, and Gravitational Waves	Ilya L. Shapiro	225-269
Basic Elements of Cosmology	Ilya L. Shapiro	271-292
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