Interdisciplinary School of Science

#### Linear Algebra

 Change of basis and linear transformations Definition of eigenvectors and eigenvalues Calculating eigenvalues and eigenvectors Diagonalisation of matrices; matrix powers Orthogonal matrices, real symmetric matrices

#### Partial Differential Equations

 Fourier Series Fourier series: Dirichlet, discontinuities and differentiation Fourier series: Weak convergence and series summation Linearity and Superposition Wave equation Heat and Diffusion equation Laplace equation and harmonic functions Fourier transform Fourier transform: properties

#### Thermodynamics

 Temperature and the Zeroth Law of Thermodynamics. Thermal equilibrium. Transport, conduction, conductivity, diffusion in gases. The two-state paramagnet and the Einstein model of a solid; quantum deviations from classical equipartition. Partition function Interacting systems, large systems, Stirling’s approximation