Mathematical Methods

These are notes from lectures on Mathematical Methods given by Prof. H.S. Green in March-May 1983. Notes given here are kept close to the original notes but additional text may be added to make it clearer. Each lecture is about one hour.

• Lecture 1 on 15 March 1983
  Arrays & affixes, symmetry of arrays, theory of determinants

• Lecture 2 on 16 March 1983
  Theory of determinants, summation convention, relations between observers and observed systems, vectors in vector space

• Lecture 3 on 17 March 1983
  Problem solving, examples of vector space, linear independence, finite-dimensional vector space, change of basis

• Lecture 4 on 22 March 1983
  Change of basis, tensor

• Lecture 5 on 23 March 1983
  Tensors, groups of transformations, group representation

• Lecture 6 on 29 March 1983
  Group representation, representation of GL(n)

• Lecture 7 on 30 March 1983
  General reduction of tensor with respect to GL(n), linear functionals

• Lecture 8 on 31 March 1983
  Summary on linear functionals, scalar product, covariant tensors, mixed tensors, contravariant metric tensor, numerical tensor

• Lecture 9 on 5 April 1983