The Absolute Differential Calculus (Calculus of Tensors) (Dover Books on Mathematics)

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.