Mathematical Geoscience

Mathematical Geoscience is an expository textbook which aims to provide a comprehensive overview of a number of different subjects within the Earth and environmental sciences. Uniquely, it treats its subjects from the perspective of mathematical modelling with a level of sophistication that is appropriate to their proper investigation. The material ranges from the introductory level, where it can be used in undergraduate or graduate courses, to research questions of current interest. The chapters end with notes and references, which provide an entry point into the literature, as well as allowing discursive pointers to further research avenues.

The introductory chapter provides a condensed synopsis of applied mathematical techniques of analysis, as used in modern applied mathematical modelling. There follows a succession of chapters on climate, ocean and atmosphere dynamics, rivers, dunes, landscape formation, groundwater flow, mantle convection, magma transport, glaciers and ice sheets, and sub-glacial floods.

This book introduces a whole range of important geoscientific topics in one single volume and serves as an entry point for a rapidly expanding area of genuine interdisciplinary research. By addressing the interplay between mathematics and the real world, this book will appeal to graduate students, lecturers and researchers in the fields of applied mathematics, the environmental sciences and engineering.

From the reviews:

“Mathematical Geoscience covers many different topics related to the earth, oceans, and atmosphere, but one can see that they all belong to the very wide field of geophysical fluid dynamics. … Each chapter contains a set of exercises. … Mathematical Geoscience is not only an excellent textbook for an advanced course in mathematical modeling for geoscientists and applied mathematicians, but also an invaluable reference for researchers, as I found out by my own experience.” (Jean-Claude Mareschal, Mathematical Geosciences, Vol. 44, 2012)

“This book … is to ‘meet the current and future needs for the interaction between various science and technology areas on the one hand and mathematics on the other.’ … aimed at graduate students, lecturers, and researchers from fields ranging from applied mathematics to the environmental sciences and engineering. … readers with a mathematical background who are interested in problems from the geosciences will most likely benefit the most. … a long but wide-ranging and interesting mathematical coverage of many important topics in geoscience.” (Neil Balmforth, SIAM Review, Vol. 54 (2), 2012)

“This interdisciplinary applied mathematics text is concerned with applications of mathematical models to diverse problems in geophysical fluid dynamics, physics and environmental science that involve ordinary and partial differential equations. … it can be used as a senior undergraduate or graduate level text in applied mathematics, physics, environmental and engineering sciences. It will definitely be useful for advanced study and research in applied mathematics, science and engineering. … This will help stimulate further study and research by students and research professionals.” (L. Debnath, Mathematical Reviews, Issue 2012 d)

“A comprehensive overview of the application of mathematical models to problems in the environment … . the book is truly amazing: topics range from climate modeling to magma transport, landscape evolution, the ocean, the atmosphere and a great deal more. … This book is a lot of fun, even just to browse. … The book is addressed to readers having some familiarity with differential equations and advanced calculus. … The exercises are another strong feature of the book: they are creative, numerous and challenging.” (William J. Satzer, The Mathematical Association of America, September, 2011)