Introduction
Mathematics of Planet Earth seems like an incredibly broad description for a course, but perhaps in order to give a rough idea of what such a course might include, we can consider the following diagram, which illustrates different categories and subject areas that are involved in the modelling of a full Earth system.
It would be possible to spend a lifetime studying any one aspects of the above categories, and they span many different areas of study, including: (i) engineering (civil, fluids, mechanical, etc.); (ii) physics (geosciences, mechanics); (iii) Earth sciences; (iv) policy and health; and so forth and so on. As mathematicians, we also have a unique perspective, and applied mathematics plays important roles in many of the above categories.
In essence, this course will include topics and themes are united by aspects of mathematical modelling and mathematical analysis and this is what distinguishes our style of study from adjacent areas of science and social science.
We will study so-called conceptual or box models of the climate. This involves some of the blue elements of the above figure, and thus we use coarse-grained models of describing the climate. This will involve applying some of the dynamical systems (phase-plane analysis of ODEs) you have learned previously, along with new methods of computation and analysis. The source for this part of the course will be (Kaper and Engler 2013).
A secondary part of this course will involve more in-depth analysis of the physical models that govern the blue elements of the above figure. This moves us from the toy box models studied above to digging into the underlying physics—this also falls into the category of Mathematical Geoscience. For example, we will use partial differential equations to study the atmosphere and develop a deeper understanding of greenhouse gases. The source for this part of the course will be (Fowler 2011).