A perturbation analysis to solve the linear equations for symmetric deformation of a deep spherical shell

In her recent Ph.D. thesis Thredgold [Jane Thredgold, Mathematical modelling of the deformation of spectacle lenses, Ph.D. thesis, University of South Australia, 2007] considers the numerical solution of equations for the deformation of a spherical shell using a finite difference methodology. In this paper, we use an elementary perturbation analysis to find an analytic solution to the linear equations for the small symmetric deformation of a deep spherical shell.