Mathematical Methods for Geophysics

Undergraduate

covers subjects required for quantitative analysis of geophysical phenomena. Vector calculus with emphasis on integral theorems is covered in the context of Maxwell's equations; Derivations and solutions of ordinary and partial differential equations with emphasis on hyperbolic, parabolic and elliptic equations in the context of the wave, heat, and potential-field equations, respectively; tensor algebra and analysis in the context of theory of elasticity and electromagnetism; Fourier analysis as a tool for solution of differential equations and signal analysis. The course may also include such topics as the calculus of variations, curvilinear coordinates on differentiable manifolds, differentiation in the sense of distributions.