Interdisciplinary School of Science
Linear Algebra
Dr. Smita Chaturvedi

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
Dr. Smita Chaturvedi

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
Dr. Smita Chaturvedi

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