Feynman path integrals are ubiquitous in quantum physics, even if a large part of the scientific community still considers them as a heuristic tool that lacks a sound mathematical definition. Our book aims to refute this prejudice, providing an extensive and self-contained description of the mathematical theory of Feynman path integration, from the earlier attempts to the latest developments, as well as its applications to quantum mechanics.This second edition presents a detailed discussion of the general theory of complex integration on infinite dimensional spaces, providing on one hand a unified view of the various existing approaches to the mathematical construction of Feynman path integrals and on the other hand a connection with the classical theory of stochastic processes. Moreover, new chapters containing recent applications to several dynamical systems have been added.This book bridges between the realms of stochastic analysis and the theory of Feynman path integration. It is accessible to both mathematicians and physicists.

With immense consumption of resources, increased global warming, and environmental pollution, the energy sector has inevitably embraced sustainability. Countries are releasing plans and programs to shift their fossil fuel-dependent energy sectors into clean energy sectors, and projections show that renewable energy will be a significant part of nations' energy mixes in the near future. Optimization and decision-making techniques have been commonly used in the energy sector as problems encountered in this sector are complex and therefore need comprehensive techniques to solve them. With the uncertainty and high-cost issues of renewable resources, the complexity increases in the sector and requires optimization and decision-making techniques. Optimization and Decision-Making in the Renewable Energy Industry analyzes renewable energy sources using current mathematical methods and techniques and provides advanced knowledge on key opportunities and challenges. The book discusses current and trending mathematical methods, tests their validity and verification, and considers their practical application in the field. Covering topics such as urban sustainability and renewable energy systems, this reference work is ideal for practitioners, academicians, industry professionals, researchers, scholars, instructors, and students.

For courses in introductory calculus-based physics. For a strong, deep, and fundamentally simple understanding of physics Eric Mazur's groundbreaking Principles and Practice of Physics establishes an understanding of physics that is thorough and accessible. Mazur's unique pedagogy and popular peer-to-peer instruction techniques incorporate insights supported by physics education research (PER) to help students develop a true conceptual understanding alongside the quantitative skills needed in the course. The material emphasizes core unifying ideas with the first half of each chapter teaching the ideas using words and images - not mathematics. The second half of each chapter casts the ideas into quantitative and symbolic form. The 2nd Edition integrates key features from the Practice volume into the Principles volume and provides all Practice volume content in Mastering Physics. The new edition provides new prelecture material that better prepares students to come to class ready to participate and supports instructors in building active and relevant lectures. Now available with Modified Mastering Physics By combining trusted author content with digital tools and a flexible platform, Mastering personalizes the learning experience and improves results for each student.

The scale transitions are essential to physical knowledge. The book describes the history of essential moments of physics, viewed as necessary consequences of the unavoidable process of scale transition, and provides the mathematical techniques for the construction of a theoretical physics founded on scale transition. The indispensable mathematical technique is analyticity, helping in the construction of space coordinate systems. The indispensable theoretical technique from physical point of view is the affine theory of surfaces. The connection between the two techniques is provided by a duality in defining the physical properties.

Spiritual Insights from the New Science is a guide to the deep spiritual wisdom drawn from one of the newest areas of science - the study of complex systems. The author, a former research scientist with over three decades of experience in the field of complexity science, tells her story of being attracted, as a young student, to the study of self-organizing systems where she encountered the strange and beautiful topics of chaos, fractals and other concepts that comprise complexity science. Using the events of her life, she describes lessons drawn from this science that provide insights into not only her own life, but all our lives. These insights show us how to weather the often disruptive events we all experience when growing and changing.The book goes on to explore, through the unfolding story of the author's life as a practicing scientist, other key concepts from the science of complex systems: cycles and rhythms, attractors and bifurcations, chaos, fractals, self-organization, and emergence. Examples drawn from religious rituals, dance, philosophical teachings, mysticism, native American spirituality, and other sources are used to illustrate how these scientific insights apply to all aspects of life, especially the spiritual. Spiritual Insights from the New Science shows the links between this new science and our human spirituality and presents, in engaging, accessible language, the argument that the study of nature can lead to a better understanding of the deepest meaning of our lives.

Advances in Applied Mechanics, Volume 53 in this ongoing series, highlights new advances in the field, with this new volume presenting interesting chapters on Phase field modelling of fracture, Advanced geometry representations and tools for microstructural and multiscale modelling, The material point method: the past and the future, From Experimental Modeling of Shotcrete to Large Scale Numerical Simulations of Tunneling, and Material point method after 25 years: theory, implementation, applications.