Interdisciplinary School of Science
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 
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 

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