Beginning: 9 am

Introduction to Tensor Calculus (ITENS)

Classification: Mathematical skills (A), general background

Lecturer: Paul Steinmann

Language: English

Contents:

* Index versus symbolic notation, coordinate representation

* Vector and tensor products

* Eigenvalue problem, invariants, spectral representation, Cayley-Hamilton theorem

* Isotropic tensor functions, representation theorems

* Gradient, divergence, rotation of tensor fields

* Integral theorems (Gauss, Stokes)

Objectives:

The students

* are familiar with the notation and coordinate representation of tensors

* are able to compute various vector and tensor products

* are familiar with the spectral representation and its consequences

* know how to compute isotropic tensor functions

* know how to compute the gradient, divergence or rotation of a tensor field

* are familiar with the relevant integral theorems