PHYS 3401 - Introduction to Mathematical Physics

• Students will be able to recognize the appearance of the operations div, grad, and curl as indicative of different physical/geometrical properties of corresponding scalar or vector fields.
• Students will be able to analyze Fourier series as a special case of an expansion in orthogonal eigenfunctions.
• Students will be able to apply vector calculus to solve specific problems, particularly in the contexts relevant for undergraduate physics courses.
• Students will be able to compute Fourier series of various simple functions, and apply Fourier series to the analysis of time-periodic phenomena.
• Students will be able to employ Laplace and Fourier transforms to solve certain ordinary differential equations and partial differential equations describing physical problems.
• Students will be able to explain the concept of eigenvalues and eigenvectors of differential operators, and their physical interpretation in specific examples.
• Students will be able to explain the relationship of functions with their Fourier transforms, to compute simple Fourier transforms in one dimension, and to interpret the Fourier transform in terms of superposition’s of momentum eigenvectors.
• Students will be able to solve classic partial differential equations of mathematical physics by the method of separation of variables.