Mathematical Journey Through Differential Equations Of Physics, A. This item is unavailable.Mathematical Journey Through Differential Equations Of Physics, A

Mathematics is the language of physics, and over time physicists have developed their own dialect. The main purpose of this book is to bridge this language barrier, and introduce the readers to the beauty of mathematical physics. It shows how to combine the strengths of both approaches: physicists often arrive at interesting conjectures based on good intuition, which can serve as the starting point of interesting mathematics. Conversely, mathematicians can more easily see commonalities between very different fields (such as quantum mechanics and electromagnetism), and employ more advanced tools.

Rather than focusing on a particular topic, the book showcases conceptual and mathematical commonalities across different physical theories. It translates physical problems to concrete mathematical questions, shows how to answer them and explains how to interpret the answers physically. For example, if two Hamiltonians are close, why are their dynamics similar?

The book alternates between mathematics- and physics-centric chapters, and includes plenty of concrete examples from physics as well as 76 exercises with solutions. It exploits that readers from either end are familiar with some of the material already. The mathematics-centric chapters provide the necessary background to make physical concepts mathematically precise and establish basic facts. And each physics-centric chapter introduces physical theories in a way that is more friendly to mathematicians.

As the book progresses, advanced material is sprinkled in to showcase how mathematics and physics augment one another. Some of these examples are based on recent publications and include material which has not been covered in other textbooks. This is to keep it interesting for the readers.

Max Lein is an associate professor and a member of the mathematics group at the interdisciplinary WPI-Advanced Institute of Materials Research of Tohoku University. He studied physics and mathematics at Technical University of Munich under the tutelage of Herbert Spohn and spent two years as a Fields Postdoctoral Fellow at the University of Toronto and the Fields Institute. Other stays included UC Berkeley, Kyushu University and the University of Tübingen.

His area of expertise are topological phenomena in condensed matter systems and classical waves as well as the derivation of effective dynamics. His research accomplishments include rigorous and non-rigorous publications alike, which have appeared in various top-level mathematics and physics journals. He has published one book with Giuseppe De Nittis on a novel mathematical approach to linear response theory.

He has extensive teaching experience and has designed several graduate-level courses from scratch — including the one this book is based on.