Principles of Continuum Applied Mathematics

3-0-9 units · Undergraduate

Covers fundamental concepts in applied mathematics and mathematical physics. Presents the major partial differential equations in physics: Laplace/Poisson, heat, wave, electromagnetism, gas and fluids dynamics, and quantum mechanics (Schrodinger). Examines derivations as models (phenomenology and continuum limits) and derivations as theories (invariance and symmetries). Discusses classical field theory, including Lagrangian densities, least-action principle, and calculus of variations. Additional topics include: tensors, covariant formalism, Delta function, Fourier series and transforms, Green's functions, and integral equations.