Mathematics for Geophysicists

Vector fields: basic vector algebra, line, surface and volume integrals, potential, conservative fields, gradient, divergence, curl, circulation, Stokes’s theorem, Gauss’s theorem, applications in fluid mechanics and electromagnetism, Kelvin’s theorem, Helmholtz’s theorem. Linear algebra: Matrices, operations, eigen components, systems of linear differential equations, examples. Partial differential equations: The diffusion equation, wave equation, Laplace’s equation, Poisson’s equation, similarity solutions, numerical solutions (simple examples with MATLAB), series solutions, spherical harmonic expansions. Dimensional analysis: Pi theorem, similarity, nondimensional formulation of geophysical problems, examples.

References

• K. F. Riley, M. P. Hobson, and S. J. Bence, Mathematical methods for physics and engineering, Cambridge University Press, 2006
• R. L. Panton, Incompressible flows, John Wiley & Sons, 2006
• F. Albarede, Introduction to geochemical modelling, Cambridge University Press, 1996. Lecture notes.