Mathematical & Computational

Directed primarily at college and university undergraduates, this book covers at basic level the essential applications of mathematics to the physical sciences. It contains all the usual topics covered in a first-year course such as vectors, matrices,...

would like to thank all those people in the life of Walter Noll I who helped me to write this book: Chancellor ofIndiana Univer- sity Professor Herman B. Wells, Dr. Klaus Andre, Professor Bemard D. Coleman, Stella DeVito, Dr. Peter Frankel, Professor...

In 1918, Emmy Noether, in her paper Invariante Variationsprobleme, proved two theorems (and their converses) on variational problems that went on to revolutionise theoretical physics. 100 years later, the mathematics of Noether's theorems continues to be...

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Statistical Mechanics is the study of systems where the number of interacting particles becomes infinite. In the last fifty years tremendous advances have been made which have required the invention of entirely new fields of mathematics such as quantum...

Adopting an elegant geometrical approach, this advanced pedagogical text describes deep and intuitive methods for understanding the subtle logic of supersymmetry while avoiding lengthy computations. The book describes how complex results and formulae...

The theory of quantum fields on curved spacetimes has attracted great attention since the discovery, by Stephen Hawking, of black-hole evaporation. It remains an important subject for the understanding of such contemporary topics as inflationary...

Research into the stability of matter has been one of the most successful chapters in mathematical physics, and is a prime example of how modern mathematics can be applied to problems in physics. A unique account of the subject, this book provides a...

The description of emerging collective phenomena and self-organization in systems composed of large numbers of individuals has gained increasing interest from various research communities in biology, ecology, robotics and control theory, as well as...

Based on lectures given in honour of Stephen Hawking's sixtieth birthday, this book comprises contributions from some of the world's leading theoretical physicists. It begins with a section containing chapters by successful scientific popularisers,...

Many people, including physicists, are confused about what the Second Law of thermodynamics really means, about how it relates to the arrow of time, and about whether it can be derived from classical mechanics. They also wonder what entropy really is: Is...

This book demonstrates some of the ways in which Microsoft Excel (R) may be used to solve numerical problems in the field of physics. But why use Excel in the first place? Certainly, Excel is never going to out-perform the wonderful symbolic algebra...

Classical field theory, which concerns the generation and interaction of fields, is a logical precursor to quantum field theory, and can be used to describe phenomena such as gravity and electromagnetism. Written for advanced undergraduates, and...

Unifying topics that are scattered throughout the literature, this book offers a definitive review of mathematical aspects of quantization and quantum field theory. It presents both basic and advanced topics of quantum field theory in a mathematically...

This is an updated and expanded second edition of a successful and well-reviewed text presenting a detailed exposition of the modern theory of supermanifolds, including a rigorous account of the super-analogs of all the basic structures of ordinary...

This is the second volume in a four-part series on fluid dynamics: Part 1. Classical Fluid Dynamics Part 2. Asymptotic Problems of Fluid Dynamics Part 3. Boundary Layers Part 4. Hydrodynamic Stability Theory The series is designed to give a comprehensive...

The quantum inverse scattering method is a means of finding exact solutions of two-dimensional models in quantum field theory and statistical physics (such as the sine-Gordon equation or the quantum non-linear Schroedinger equation). These models are the...

Mathematics plays a fundamental role in the formulation of physical theories. This textbook provides a self-contained and rigorous presentation of the main mathematical tools needed in many fields of Physics, both classical and quantum. It covers topics...

This book, an abridgment of Volumes I and II of the highly respected Group Theory in Physics, presents a carefully constructed introduction to group theory and its applications in physics. The book provides anintroduction to and description of the most...

Essential Dynamics & Relativity provides students with an introduction to the core aspects of dynamics and special relativity. The author reiterates important ideas and terms throughout and covers concepts that are often missing from other textbooks at...

Anomalous diffusion has been detected in a wide variety of scenarios, from fractal media, systems with memory, transport processes in porous media, to fluctuations of financial markets, tumour growth, and complex fluids. Providing a contemporary...

Self-contained and comprehensive, this definitive new edition of Gravity and Strings is a unique resource for graduate students and researchers in theoretical physics. From basic differential geometry through to the construction and study of black-hole...

This text is designed for an intermediate-level, two-semester undergraduate course in mathematical physics. It provides an accessible account of most of the current, important mathematical tools required in physics these days. It is assumed that the...

Networks are convenient mathematical models to represent the structure of complex systems, from cells to societies. In the last decade, multilayer network science - the branch of the field dealing with units interacting in multiple distinct ways,...

An algebraic structure consists of a set of elements, with some rule of combining them, or some special property of selected subsets of the entire set. Many algebraic structures, such as vector space and group, come to everyday use of a modern physicist...

This book aims to fill the gap in the available literature on supermanifolds, describing the different approaches to supermanifolds together with various applications to physics, including some which rely on the more mathematical aspects of supermanifold...

A paperback edition of a classic text, this book gives a unique survey of the known solutions of Einstein's field equations for vacuum, Einstein-Maxwell, pure radiation and perfect fluid sources. It introduces the foundations of differential geometry and...

In the last decade, there have been an increasing convergence of interest and methods between theoretical physics and fields as diverse as probability, machine learning, optimization and compressed sensing. In particular, many theoretical and applied...

Vectors and tensors are among the most powerful problem-solving tools available, with applications ranging from mechanics and electromagnetics to general relativity. Understanding the nature and application of vectors and tensors is critically important...

This book is an introduction to the theory, practice, and implementation of the Lattice Boltzmann (LB) method, a powerful computational fluid dynamics method that is steadily gaining attention due to its simplicity, scalability, extensibility, and simple...

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This undergraduate textbook provides a simple, concise introduction to tensor algebra and analysis, as well as special and general relativity. With a plethora of examples, explanations, and exercises, it forms a well-rounded didactic text that will be...

The availability of large data sets has allowed researchers to uncover complex properties such as large-scale fluctuations and heterogeneities in many networks, leading to the breakdown of standard theoretical frameworks and models. Until recently these...

Introduction to the Maths and Physics of Quantum Mechanics details the mathematics and physics that are needed to learn the principles of quantum mechanics.It provides an accessible treatment of how to use quantum mechanics and why it is so successful in...

This book provides an introductory albeit solid presentation of path integration techniques as applied to the field of stochastic processes. The subject began with the work of Wiener during the 1920's, corresponding to a sum over random trajectories,...

Boundary conformal field theory is concerned with a class of two-dimensional quantum field theories which display a rich mathematical structure and have many applications ranging from string theory to condensed matter physics. In particular, the...

This book is a course in methods and models rooted in physics and used in modelling economic and social phenomena. It covers the discipline of econophysics, which creates an interface between physics and economics. Besides the main theme, it touches on...

This book aims to provide a quick pedagogical introduction to path integrals. It contains original material that never before has appeared in a book, for example the path integrals for the Wigner functions and for Classical Mechanics. This application to...

This volume contains a collection of papers based on lectures delivered by distinguished mathematicians at Clay Mathematics Institute events over the past few years. It is intended to be the first in an occasional series of volumes of CMI lectures...

Building on the material learned by students in their first few years of study, Topics in Statistical Mechanics (Second Edition) presents an advanced level course on statistical and thermal physics. It begins with a review of the formal structure of...