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The Absolute Differential Calculus (Calculus of Tensors) (Dover Books on Mathematics), by Tullio Levi-Civita
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Written by a towering figure of twentieth-century mathematics, this classic examines the mathematical background necessary for a grasp of relativity theory. Tullio Levi-Civita provides a thorough treatment of the introductory theories that form the basis for discussions of fundamental quadratic forms and absolute differential calculus, and he further explores physical applications.
Part one opens with considerations of functional determinants and matrices, advancing to systems of total differential equations, linear partial differential equations, algebraic foundations, and a geometrical introduction to theory. The second part addresses covariant differentiation, curvature-related Riemann's symbols and properties, differential quadratic forms of classes zero and one, and intrinsic geometry. The final section focuses on physical applications, covering gravitational equations and general relativity.
- Sales Rank: #749191 in eBooks
- Published on: 2013-07-24
- Released on: 2013-07-24
- Format: Kindle eBook
Language Notes
Text: English, Italian (translation)
About the Author
Italian mathematician Tullio Levi-Civita (1873–1941) is most famous for his work on absolute differential calculus and its applications to relativity theory.
Most helpful customer reviews
11 of 14 people found the following review helpful.
An excellent book governing the mathematical beasts; tensors
By A Customer
A must have for all physics majors. Excellent outside source for mechanics, especially upper-division.
8 of 10 people found the following review helpful.
A book that returns you to the unbounded rigor of calculus
By A Customer
Not quite a page-turner, but this book presents good applications of tensor math. Sometimes difficult to follow, the book omits many "assumed" steps. However, a fine escape into the world of absolute differential calculus.
5 of 6 people found the following review helpful.
Original Paper
By Francesco Erriques
This book constitutes the history of Absolute Differential Calculus, born from the cooperation from Albert Einstein and Tullio Levi Civita. It also keeps an account on what Gregorio Ricci Curbastro had previously estabilished on Tensors. I think it's a wonderful occasion, to study from the original papers of the authors of a theory, though they are generally somehow obscure, with respect to textbooks. This is definitely a great book.
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