Because it is grounded in math, chemical thermodynamics is often perceived as a difficult subject and many students are never fully comfortable with it. The first authoritative textbook presentation of equilibrium chemical and phase thermodynamics in a reformulated geometrical framework, Chemical and Phase Thermodynamics shows how this famously difficult subject can be accurately expressed with only elementary high-school geometry concepts. Featuring numerous suggestions for research-level extensions, this simplified alternative to standard calculus-based thermodynamics expositions is perfect for undergraduate and beginning graduate students as well as researchers.

The aim of the book is to treat all three basic theories of physics, namely, classical mechanics, statistical mechanics, and quantum mechanics from the same perspective, that of symplectic geometry, thus showing the unifying power of the symplectic geometric approach. Reading this book will give the reader a deep understanding of the interrelationships between the three basic theories of physics. This book is addressed to graduate students and researchers in mathematics and physics who are interested in mathematical and theoretical physics, symplectic geometry, mechanics, and (geometric) quantization.

This is a self-contained introductory textbook on the calculus of differential forms and modern differential geometry. The intended audience is physicists, so the author emphasises applications and geometrical reasoning in order to give results and concepts a precise but intuitive meaning without getting bogged down in analysis. The large number of diagrams helps elucidate the fundamental ideas. Mathematical topics covered include differentiable manifolds, differential forms and twisted forms, the Hodge star operator, exterior differential systems and symplectic geometry. All of the mathematics is motivated and illustrated by useful physical examples.

This volume presents lectures given at the Summer School Wisła 18: Nonlinear PDEs, Their Geometry, and Applications, which took place from August 20 - 30th, 2018 in Wisła, Poland, and was organized by the Baltic Institute of Mathematics. The lectures in the first part of this volume were delivered by experts in nonlinear differential equations and their applications to physics. Original research articles from members of the school comprise the second part of this volume. Much of the latter half of the volume complements the methods expounded in the first half by illustrating additional applications of geometric theory of differential equations. Various subjects are covered, providing readers a glimpse of current research. Other topics covered include thermodynamics, meteorology, and the Monge–Ampère equations. Researchers interested in the applications of nonlinear differential equations to physics will find this volume particularly useful. A knowledge of differential geometry is recommended for the first portion of the book, as well as a familiarity with basic concepts in physics.

This volume arose from a semester at CIRM-Luminy on “Thermodynamic Formalism: Applications to Probability, Geometry and Fractals” which brought together leading experts in the area to discuss topical problems and recent progress. It includes a number of surveys intended to make the field more accessible to younger mathematicians and scientists wishing to learn more about the area. Thermodynamic formalism has been a powerful tool in ergodic theory and dynamical system and its applications to other topics, particularly Riemannian geometry (especially in negative curvature), statistical properties of dynamical systems and fractal geometry. This work will be of value both to graduate students and more senior researchers interested in either learning about the main ideas and themes in thermodynamic formalism, and research themes which are at forefront of research in this area.

This textbook is for a one semester introductory course in thermodynamics, primarily for use in a mechanical or aerospace engineering program, although it could also be used in an engineering science curriculum. The book contains a section on the geometry of curves and surfaces, in order to review those parts of calculus that are needed in thermodynamics for interpolation and in discussing thermodynamic equations of state of simple substances. It presents the First Law of Thermodynamics as an equation for the time rate of change of system energy, the same way that Newton’s Law of Motion, an equation for the time rate of change of system momentum, is presented in Dynamics. Moreover, this emphasis illustrates the importance of the equation to the study of heat transfer and fluid mechanics. New thermodynamic properties, such as internal energy and entropy, are introduced with a motivating discussion rather than by abstract postulation, and connection is made with kinetic theory. Thermodynamic properties of the vaporizable liquids needed for the solution of practical thermodynamic problems (e.g. water and various refrigerants) are presented in a unique tabular format that is both simple to understand and easy to use. All theoretical discussions throughout the book are accompanied by worked examples illustrating their use in practical devices. These examples of the solution of various kinds of thermodynamic problems are all structured in exactly the same way in order to make, as a result of the repetitions, the solution of new problems easier for students to follow, and ultimately, to produce themselves. Many additional problems are provided, half of them with answers, for students to do on their own.