Helmholtz equation

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Introduces ordinary differential equations of higher order and their solutions with initial conditions.

Explores the Frenet-Serret formulas for curvature and torsion in three-dimensional space.

Explores the history of lasers and the Lorentz model for atom-light interaction.

Explores MHD equilibrium and stability, emphasizing energy considerations for determining stability.

Explores linear differential equations of order n, including homogeneous and inhomogeneous equations, solutions, and linear independence.

Covers the generalities of functions, including the definition of an application between sets and the uniqueness of elements in the image set.

Introduces the Frobenius method for solving second-order linear ODEs around ordinary points.

Covers heat equations, Fourier transforms, and variable separation methods.

Explores diagonalization of moment of inertia and principal directions in orthonormal base vectors.

Explores polymer collapse, emphasizing covolume and free energy in the process.