Mathematical Methods for Physics

Solve first-order and second-order linear ordinary differential equations (ODEs) with constant coefficients.

Represent periodic functions using Fourier series and calculate their coefficients.

Define and apply the gradient, divergence, and curl operators to scalar and vector fields in Cartesian coordinates.

Evaluate line integrals to calculate work done by a vector field along a specified path.

Evaluate surface integrals to calculate flux of a vector field through a given surface.

Evaluate volume integrals to determine properties of three-dimensional regions.

Apply the Divergence Theorem (Gauss's Theorem) to relate volume and surface integrals.

Apply Stokes' Theorem to relate surface and line integrals.