David D. Nolte

Introduction to Modern Dynamics: From Classical Mechanics to Complex Systems offers a comprehensive and unified perspective on dynamics for the 21st century. Now in its third edition, the text provides a rigorous yet accessible foundation in Lagrangian and Hamiltonian mechanics, modernized with a geometric viewpoint that enhances intuitive understanding. The book's four-part structure provides a seamless transition from foundational principles to cutting-edge topics, beginning with the foundations of classical and complex mechanics and moving on to cover applications of those concepts to complex systems, as well as relativity and spacetime. To facilitate student learning and prepare them for careers in research and technology, this edition has a renewed focus on practical application. Each chapter includes numerous worked problems, and online access to computational code allows students to explore a wealth of nonlinear phenomena. These resources are designed to equip students with the analytical and computational skills necessary to tackle the complex dynamical systems that are increasingly central to science and technology, while continuing the tradition of classical mechanics as the common language for practicing physicists.

Introduction to Modern Dynamics: From Classical Mechanics to Complex Systems offers a comprehensive and unified perspective on dynamics for the 21st century. Now in its third edition, the text provides a rigorous yet accessible foundation in Lagrangian and Hamiltonian mechanics, modernized with a geometric viewpoint that enhances intuitive understanding. The book's four-part structure provides a seamless transition from foundational principles to cutting-edge topics, beginning with the foundations of classical and complex mechanics and moving on to cover applications of those concepts to complex systems, as well as relativity and spacetime. To facilitate student learning and prepare them for careers in research and technology, this edition has a renewed focus on practical application. Each chapter includes numerous worked problems, and online access to computational code allows students to explore a wealth of nonlinear phenomena. These resources are designed to equip students with the analytical and computational skills necessary to tackle the complex dynamical systems that are increasingly central to science and technology, while continuing the tradition of classical mechanics as the common language for practicing physicists.

Ever wonder why soap bubbles become invisible right before they pop? Or why lenses are so blue they look purple? How is it possible to image black holes at the heart of distant galaxies? The answer to all these questions is Interference. This book tells the story of the science of optical interferometry - mankind's most sensitive form of measurement - and of the scientists who tamed light to make outstanding discoveries, from lasers and holograms to astronomy and quantum physics. In the past several years, interferometry has been used to discover exoplanets orbiting distant stars, to take the first image of a black hole, to detect the first gravitational waves and to create the first programmable quantum computer. This list of achievements points to the fertile and active field of interferometry for which this book provides a convenient and up - to - date guide for a wide audience interested in the science of light.

The best parts of physics are the last topics that our students ever see. These are the exciting new frontiers of nonlinear and complex systems that are at the forefront of university research and are the basis of many high-tech businesses. Topics such as traffic on the World Wide Web, the spread of epidemics through globally-mobile populations, or how the synchronization of global economies are governed by universal principles just as profound as Newton's laws. Nonetheless, the conventional university physics curriculum reserves most of these topics for graduate study because of the assumed need for advanced mathematics. However, by using only linear algebra and calculus, combined with exploratory computer simulations, all of these topics become accessible to advanced undergraduate students. The structure of this book combines the three main topics of modern dynamics - chaos theory, dynamics on complex networks, and general relativity - into a coherent framework. By taking a geometric view of physics, concentrating on the time evolution of physical systems as trajectories through abstract spaces, these topics share a common and simple mathematical language through which any student can gain a unified physical intuition. Given the growing importance of complex dynamical systems in many areas of science and technology, this text provides students with an up-to-date foundation for their future careers. This second edition has an updated introductory chapter and has added key topics to help students prepare for their GRE physics subject exam. It also has expanded chapters on Hamiltonian dynamics, Hamiltonian chaos, and Econophysics, while increasing the number of homework problems at the end of each chapter. The second edition is designed to fulfill the textbook needs of any advanced undergraduate course in mechanics.

The best parts of physics are the last topics that our students ever see. These are the exciting new frontiers of nonlinear and complex systems that are at the forefront of university research and are the basis of many high-tech businesses. Topics such as traffic on the World Wide Web, the spread of epidemics through globally-mobile populations, or how the synchronization of global economies are governed by universal principles just as profound as Newton's laws. Nonetheless, the conventional university physics curriculum reserves most of these topics for graduate study because of the assumed need for advanced mathematics. However, by using only linear algebra and calculus, combined with exploratory computer simulations, all of these topics become accessible to advanced undergraduate students. The structure of this book combines the three main topics of modern dynamics - chaos theory, dynamics on complex networks, and general relativity - into a coherent framework. By taking a geometric view of physics, concentrating on the time evolution of physical systems as trajectories through abstract spaces, these topics share a common and simple mathematical language through which any student can gain a unified physical intuition. Given the growing importance of complex dynamical systems in many areas of science and technology, this text provides students with an up-to-date foundation for their future careers. This second edition has an updated introductory chapter and has added key topics to help students prepare for their GRE physics subject exam. It also has expanded chapters on Hamiltonian dynamics, Hamiltonian chaos, and Econophysics, while increasing the number of homework problems at the end of each chapter. The second edition is designed to fulfill the textbook needs of any advanced undergraduate course in mechanics.

Galileo Unbound traces the journey that brought us from Galileo's law of free fall to today's geneticists measuring evolutionary drift, entangled quantum particles moving among many worlds, and our lives as trajectories traversing a health space with thousands of dimensions. Remarkably, common themes persist that predict the evolution of species as readily as the orbits of planets or the collapse of stars into black holes. This book tells the history of spaces of expanding dimension and increasing abstraction and how they continue today to give new insight into the physics of complex systems. Galileo published the first modern law of motion, the Law of Fall, that was ideal and simple, laying the foundation upon which Newton built the first theory of dynamics. Early in the twentieth century, geometry became the cause of motion rather than the result when Einstein envisioned the fabric of space-time warped by mass and energy, forcing light rays to bend past the Sun. Possibly more radical was Feynman's dilemma of quantum particles taking all paths at once -- setting the stage for the modern fields of quantum field theory and quantum computing. Yet as concepts of motion have evolved, one thing has remained constant, the need to track ever more complex changes and to capture their essence, to find patterns in the chaos as we try to predict and control our world.

This book presents the fundamental physics of optical interferometry as applied to biophysical, biological and medical research. Interference is at the core of many types of optical detection and is a powerful probe of cellular and tissue structure in interfererence microscopy and in optical coherence tomography. It is also the root cause of speckle and other imaging artefacts that limit range and resolution. For biosensor applications, the inherent sensitivity of interferometry enables ultrasensitive detection of molecules in biological samples for medical diagnostics. In this book, emphasis is placed on the physics of light scattering, beginning with the molecular origins of refraction as light propagates through matter, and then treating the stochastic nature of random fields that ultimately dominate optical imaging in cells and tissue. The physics of partial coherence plays a central role in the text, with a focus on coherence detection techniques that allow information to be selectively detected out of incoherent and heterogeneous backgrounds. Optical Interferometry for Biology and Medicine is divided into four sections. The first covers fundamental principles, and the next three move up successive scales, beginning with molecular interferometry (biosensors), moving to cellular interferometry (microscopy), and ending with tissue interferometry (biomedical). An outstanding feature of the book is the clear presentation of the physics, with easy derivations of the appropriate equations, while emphasizing "rules of thumb" that can be applied by experimental researchers to give semi-quantitative predictions.

The best parts of physics are the last topics that our students ever see. These are the exciting new frontiers of nonlinear and complex systems that are at the forefront of university research and are the basis of many high-tech businesses. Topics such as traffic on the World Wide Web, the spread of epidemics through globally-mobile populations, or the synchronization of global economies are governed by universal principles just as profound as Newton's laws. Nonetheless, the conventional university physics curriculum reserves most of these topics for advanced graduate study. Two justifications are given for this situation: first, that the mathematical tools needed to understand these topics are beyond the skill set of undergraduate students, and second, that these are speciality topics with no common theme and little overlap. Introduction to Modern Dynamics dispels these myths. The structure of this book combines the three main topics of modern dynamics - chaos theory, dynamics on complex networks, and general relativity - into a coherent framework. By taking a geometric view of physics, concentrating on the time evolution of physical systems as trajectories through abstract spaces, these topics share a common and simple mathematical language through which any student can gain a unified physical intuition. Given the growing importance of complex dynamical systems in many areas of science and technology, this text provides students with an up-to-date foundation for their future careers.

The best parts of physics are the last topics that our students ever see. These are the exciting new frontiers of nonlinear and complex systems that are at the forefront of university research and are the basis of many high-tech businesses. Topics such as traffic on the World Wide Web, the spread of epidemics through globally-mobile populations, or the synchronization of global economies are governed by universal principles just as profound as Newton's laws. Nonetheless, the conventional university physics curriculum reserves most of these topics for advanced graduate study. Two justifications are given for this situation: first, that the mathematical tools needed to understand these topics are beyond the skill set of undergraduate students, and second, that these are speciality topics with no common theme and little overlap. Introduction to Modern Dynamics dispels these myths. The structure of this book combines the three main topics of modern dynamics - chaos theory, dynamics on complex networks, and general relativity - into a coherent framework. By taking a geometric view of physics, concentrating on the time evolution of physical systems as trajectories through abstract spaces, these topics share a common and simple mathematical language through which any student can gain a unified physical intuition. Given the growing importance of complex dynamical systems in many areas of science and technology, this text provides students with an up-to-date foundation for their future careers.

This book presents the fundamental physics of optical interferometry as applied to biophysical, biological and medical research. Interference is at the core of many types of optical detection and is a powerful probe of cellular and tissue structure in interfererence microscopy and in optical coherence tomography. It is also the root cause of speckle and other imaging artefacts that limit range and resolution. For biosensor applications, the inherent sensitivity of interferometry enables ultrasensitive detection of molecules in biological samples for medical diagnostics. In this book, emphasis is placed on the physics of light scattering, beginning with the molecular origins of refraction as light propagates through matter, and then treating the stochastic nature of random fields that ultimately dominate optical imaging in cells and tissue. The physics of partial coherence plays a central role in the text, with a focus on coherence detection techniques that allow information to be selectively detected out of incoherent and heterogeneous backgrounds. Optical Interferometry for Biology and Medicine is divided into four sections. The first covers fundamental principles, and the next three move up successive scales, beginning with molecular interferometry (biosensors), moving to cellular interferometry (microscopy), and ending with tissue interferometry (biomedical). An outstanding feature of the book is the clear presentation of the physics, with easy derivations of the appropriate equations, while emphasizing "rules of thumb" that can be applied by experimental researchers to give semi-quantitative predictions.