The Absolute Differential Calculus (calculus Of Tensors) (dover Books On Mathematics)
by Tullio Levi-Civita /
2013 / English / DjVu
3.5 MB Download
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.
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.
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.
