The Absolute Differential Calculus (Calculus of Tensors)

Nonfiction, Science & Nature, Mathematics, Vector Analysis, Calculus
Cover of the book The Absolute Differential Calculus (Calculus of Tensors) by Tullio Levi-Civita, Dover Publications
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Author: Tullio Levi-Civita ISBN: 9780486316253
Publisher: Dover Publications Publication: July 24, 2013
Imprint: Dover Publications Language: English
Author: Tullio Levi-Civita
ISBN: 9780486316253
Publisher: Dover Publications
Publication: July 24, 2013
Imprint: Dover Publications
Language: English

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.

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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.

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