The impact of quantum mechanics on our day-to-day life is growing at an exponential rate, of which most people are unaware. For example, the toaster is a prime example of a quantum mechanical device. While quantum mechanics arose as a subject in physics, quantum mechanical thinking has had, and continues to have, a broad impact on mathematics. For example, operator theory as we know it today would not exist without von Neumann's effort to put quantum mechanics on a solid mathematical found...

Chemical reaction dynamics is crucial for the study of chemical processes and the mechanisms which govern them. Most frameworks, however, remain static when representing the landscape of chemical reactions, falling short of capturing fully the evolution over time of the reaction profile.This book presents an application of fundamental mathematical theories — dynamical systems theory and phase space — to chemical reaction dynamics. These concepts are relevant to the analysis of chem...

Ordinary differential equations is a standard course in the undergraduate mathematics curriculum that usually comes after the first university calculus and linear algebra courses taken by a mathematics major. Such courses may also typically be attended by undergraduates from other areas of physical and social sciences, and engineering. The content of such a course has remained fairly static over time, despite the expansion of the topic into other disciplines as a result of the dynamical sy...

This book develops elementary classical mechanics in a setting that is appropriate for beginning university mathematics students without requiring a background in physics. It is an ideal first look at the subject for those who will go on to study more advanced aspects of the subject, such as Lagrangian, Hamiltonian, and quantum mechanics. These more advanced developments of mechanics are at the forefront of research in modern mathematics. Certainly, topics such as symplectic geometry, Lagr...

This Problems and Solutions book addresses the numerous problems in the textbook that develops elementary classical mechanics in a setting that is appropriate for beginning university mathematics students without requiring a background in physics. It is an ideal first look at the subject for those who will go on to study more advanced aspects of the subject, such as Lagrangian, Hamiltonian, and quantum mechanics. These more advanced developments of mechanics are at the forefront of researc...

This concise book introduces nonphysicists to the core philosophical issues surrounding the nature and structure of space and time, and is also an ideal resource for physicists interested in the conceptual foundations of space-time theory.Tim Maudlin's broad historical overview examines Aristotelian and Newtonian accounts of space and time, and traces how Galileo's conceptions of relativity and space-time led to Einstein's special and general theories of relativity. Maudlin explain...

Quantum physics is believed to be the fundamental theory underlying our understanding of the physical universe. However, it is based on concepts and principles that have always been difficult to understand and controversial in their interpretation. This book aims to explain these issues using a minimum of technical language and mathematics. After a brief introduction to the ideas of quantum physics, the problems of interpretation are identified and explained. The rest of the book surveys, ...

A concise but rigorous treatment of variational techniques, focussing primarily on Lagrangian and Hamiltonian systems, this book is ideal for physics, engineering and mathematics students. The book begins by applying Lagrange's equations to a number of mechanical systems. It introduces the concepts of generalized coordinates and generalized momentum. Following this the book turns to the calculus of variations to derive the Euler–Lagrange equations. It introduces Hamilton's principle and us...

This book is an account of my first encounter with Einstein's Special Relativity. It is inevitable that in trying to unravel the theory's logical inconsistencies I did not at first attempt succeed in correcting it. The logic does not stand the test of a detailed follow through. Our fundamental understanding of relativity in the universe is thus still waiting to be put right. Patience. (Feb. 2019)

Note: The three volumes are not sequential but rather independent of each other and largely self-contained.Perturbed Evolution has a closer link to Simple Systems than that volume has to Basic Matters, but any reader familiar with the subject matter of a solid introduction to quantum mechanics - such as Dirac's formalism of kets and bras, Schrödinger's and Heisenberg's equations of motion, and the standard examples that can be treated exactly, with harmonic oscillators and hydrogen-like at...

Special relativity provides the foundations of our knowledge of space and time. Without it, our understanding of the world, and its place in the universe, would be unthinkable. This book gives a concise, elementary, yet exceptionally modern, introduction to special relativity. It is a gentle yet serious 'first encounter', in that it conveys a true understanding rather than purely reports the basic facts. Only very elementary mathematical knowledge is needed to master it (basic high-school ...

The second edition of A First Course in Integral Equations integrates the newly developed methods with classical techniques to give modern and robust approaches for solving integral equations. The manual accompanying this edition contains solutions to all exercises with complete step-by-step details. To interested readers trying to master the concepts and powerful techniques, this manual is highly useful, focusing on the readers' needs and expectations. It contains the same notations used ...