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Prof B Monserrat

The aim of this course is revision of mathematics. The course booklet contains a comprehensive handout for the course. It is assumed that you have a working knowledge of trigonometry, and of the basic principles and practice of differentiation and integration. The course draws heavily on examples taken from materials science where the ability to use mathematics as a tool can be usefully illustrated.

It is recommended that you work through the problems with your supervision group or other Part II students and then use to supervision to focus on the subjects and problems you found challenging.

The course will cover:

  • Direction cosines
  • Matrix algebra
  • Principal axes, eigenvalues and eigenvectors
  • Matrix transformations
  • Delta functions
  • Fourier series, Fourier transforms and convolution
  • Series expansions and summations
  • Statistics and error handling
  • Differentiation of exponentials
  • Lagrange multipliers
  • Second order linear differential equations
  • Solutions of first-order differential equations
  • Applications of differential equations to diffusion and solidification