MA622
Tensor Analysis and Differentiable Manifolds
0.5 Credit

This course introduces tensor analysis with differential geometry and variational calculus for modelling static and dynamical problems. Topics include: vector spaces; affine tensor algebras of arbitrary rank; covariant and contravariant vectors and tensors; cartesian and non-cartesian tensor algebras; symmetries under linear and nonlinear coordinate transformations; tensor fields and their derivatives; tensor analysis on manifolds; differential forms. Additional topics may include Lie differentiation; generalized Stokes' theorem; Riemannian manifolds. Applications of tensors and manifolds may include: the analysis of invariance properties arising in physical phenomena; geodesic flow; Hamilton-Jacobi theory and classical and quantum field theories.