A Primer in Tensor Analysis and Relativity
This undergraduate textbook provides a simple, concise introduction to tensor algebra and analysis, as well as special and general relativity. With a plethora of examples, explanations, and exercises, it forms a well-rounded didactic text that will be useful for any related course. The book is divid...
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| Format: | Electronic eBook |
| Language: | English |
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Cham :
Springer International Publishing : Imprint: Springer,
2019.
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| Edition: | 1st ed. 2019. |
| Series: | Undergraduate Lecture Notes in Physics,
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| Online Access: | Full Text via HEAL-Link |
Table of Contents:
- Acknowledgements
- Preface
- Part I: Tensor Algebra and Analysis
- 1: Linear spaces, vectors and tensors
- 2: Operations over tensors, metric tensor
- 3: Symmetric, skew(anti) symmetric tensors and determinants
- 4: Curvilinear coordinates, local coordinate transformations
- 5: Derivatives of tensors, covariant derivates
- 6: Grad, div, rot and relations between them
- 7: Grad, div, rot and in cylindric and spherical coordinates
- 8: Curvilinear, surface and D-dimensional integrals
- 9: Theorems of Green, Stokes and Gauss
- 10: Solutions to the exercises from Part 1
- Part II: Elements of Electrodynamics and Special Relativity
- 11 Maxwell equations and Lorentz transformations
- 12 Laws of relativistic mechanics
- 13 Maxwell equations in relativistic form
- Part III Applications to General Relativity
- 14 Equivalence principle, covariance and curvature tensor
- 15 Einstein equations, Schwarzschild solution and gravitational waves
- 16 Basic elements of cosmology
- 17 Special sections
- Index.
