Title
The Absolute Differential Calculus (Calculus of Tensors) (Dover Books on Mathematics),Used
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Written by a towering figure of twentiethcentury mathematics, this classic examines the mathematical background necessary for a grasp of relativity theory. Tullio LeviCivita 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, curvaturerelated 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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