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Covers the application of separation of variables method to solve the heat equation.

Covers partial differential equations, Hessians, and the Implicit Function Theorem, with a focus on exam question resolution.

Explores transduction and downmixing in micro/nanomechanical devices, focusing on noise sources and signal processing.

Covers advanced topics in physics, focusing on oscillations and dynamics, including the harmonic oscillator and forced oscillations.

Explores derivability and continuity of functions, showcasing examples of functions with differentiability properties.

Covers the solution of linear second order ODEs with constant coefficients and explores the method of variation of parameters.

Explores quantum optics of resonators, covering cavity Hamiltonian, quantum Langevin equations, Purcell effect, and cavity QED.

Explores trigonometric polynomials, periodicity, and Fourier coefficients in mathematical analysis.

Covers the concept of limits and continuity in real analysis.

Series covers spherical coordinates, harmonics, Legendre polynomials, and angular momentum.