Concluding Capstone Problems

Abstract

In closing, five capstone problems are offered in this chapter. They deal with the propagation of a noncytopathic virus in a target cell population, Jeans’ criterion for the occurrence of a self-gravitational instability in a rotating inviscid adiabatic gas cloud of infinite extent, the critical conditions for the onset of a Rayleigh–Bénard instability in a Boussinesq dissociating gas layer at chemical quasi-equilibrium being heated from below or above, a complex nonlinear stability expansion of the model equation which was analyzed by a real expansion approach in Problem 16.1, and an exact solution of the Black–Scholes heat-type partial differential equation of mathematical finance. Each of these problems synthesize several concepts presented in earlier chapters and as such they serve as a fitting conclusion to this book on comprehensive applied mathematical modeling given that the first three are data-driven, the fourth allows a comparison between two different methods of analysis, and the fifth exhibits how techniques developed for the natural and engineering sciences can be applied to a quantitative finance phenomenon.