Mathematical Modelling with Differential Equations aims to introduce various strategies for modelling systems using differential equations. Some of these methodologies are elementary and quite direct to comprehend and apply while others are complex in nature and require thoughtful, deep contemplation. Many topics discussed in the chapter do not appear in any of the standard textbooks and this provides users an opportunity to consider a more general set of interesting systems that can be modelled. For example, the book investigates the evolution of a "toy universe," discusses why "alternate futures" exists in classical physics, constructs approximate solutions to the famous Thomas—Fermi equation using only algebra and elementary calculus, and examines the importance of "truly nonlinear" and oscillating systems.
Features