A Primer in Tensor Analysis and Relativity

• Κύριος συγγραφέας: Shapiro, Ilya L. (Συγγραφέας, http://id.loc.gov/vocabulary/relators/aut)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Cham : Springer International Publishing : Imprint: Springer, 2019.
• Έκδοση: 1st ed. 2019.
• Σειρά: Undergraduate Lecture Notes in Physics,
• Θέματα: Physics.; Gravitation.; Optics.; Electrodynamics.; Mathematical physics.; Quantum field theory.; String theory.; Mathematical Methods in Physics.; Classical and Quantum Gravitation, Relativity Theory.; Classical Electrodynamics.; Mathematical Physics.; Numerical and Computational Physics, Simulation.; Quantum Field Theories, String Theory.

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...

Πίνακας περιεχομένων:

• 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.