This book presents a selection of the best contributions to GIREP EPEC 2015, the Conference of the International Research Group on Physics Teaching (GIREP) and the European Physical Society's Physics Education Division (EPS PED). It introduces readers interested in the field to the problem of identifying strategies and tools to improve physics teaching and learning so as to convey Key Competences and help students acquire them. The main topic of the conference was Key Competences (KC) in physics teaching and learning in the form of knowledge, skills and attitudes that are fundamental for every member of society. Given the role of physics as a field strongly connected not only to digital competence but also to several other Key Competences, this conference provided a forum for in-depth discussions of related issues.

Energy is a key source of economic growth due to its involvement as the primary input. Energy drives economic productivity and industrial growth. It can be considered as the prime requirement for the modern economy. Solar energy is a renewable source of energy that can be used to produce heat or generate electricity. The total amount of solar energy available on Earth’s surface is vastly in excess of the world’s current and anticipated energy requirements. In the 21st century, solar energy is expected to become increasingly attractive as a renewable energy source. An increase in the share of solar energy may destabilize the grid. To overcome the issues of grid instability, specifically in remote areas, BIM and GIS-based microgrid planning based on data can be effectively used. BIM and GIS are used to assess alternative solutions and big data analytics in building solar electrical systems according to planning requirements and managing assets. The integration of BIM and GIS information systems for microgrid planning is appealing due to its potential benefits, such as it decreases the microgrid planning time and cost. The present book is about the advancements in technology for harnessing solar energy and the challenges associated with different modes of utilizing this inexhaustible renewable energy source. This book will be helpful for researchers, academicians, technologists, innovators, and industry experts working in the area of solar energy, artificial intelligence, and smart grids.

This new book from one of the most published authors in all of mathematics is an attempt to offer a new, more modern take on the Differential Equations course. The world is changing. Because of the theory of wavelets, Fourier analysis is ever more important and central. And applications are a driving force behind much of mathematics.This text text presents a more balanced picture. The text covers differential equations (both ordinary and partial), Fourier analysis and applications in equal measure and with equal weight. The Riemann integral is used throughout. We do not assume that the student knows any functional analysis. We likewise do not assume that the student has had a course in undergraduate real analysis. To make the book timely and exciting, a substantial chapter on basic properties of wavelets, with applications to signal processing and image processing is included. This should give students and instructors alike a taste of what is happening in the subject today.

The last lecture course that Nobel Prize winner Richard P. Feynman gave at Caltech from 1983 to 1986 was not on physics but on computer science. The first edition of the Feynman Lectures on Computation published in 1996 and provided an overview of standard and not-so-standard topics in computer science given in Feynman's inimitable style. Although now over 20 years old, most of the material is still relevant and interesting, and Feynman's unique philosophy of learning and discovery shines through. For this new edition, Tony Hey has updated the lectures with an invited chapter from Professor John Preskill on "Quantum Computing 40 Years Later." This contribution captures the progress made towards building a quantum computer since Feynman's original suggestions in 1981. The last 25 years have also seen the "Moore's Law" roadmap for the IT industry coming to an end. To reflect this transition, John Shalf, Senior Scientist at Lawrence Berkeley National Laboratory, has contributed a chapter on "The Future of Computing Beyond Moore's Law." The final update for this edition capturea Feynman's interest in Artificial Intelligence and Artificial Neural Networks. Eric Mjolsness, now a professor of Computer Science at the University of California Irvine, was a Teaching Assistant for Feynman's original lecture course and his research interests are now in the application of Artificial Intelligence and Machine Learning for multi-scale science. He has contributed a chapter on "Feynman on Artificial Intelligence and Machine Learning" that captures the early discussions with Feynman and also looks towards future developments. This exciting and important work provides key reading for students and scholars in the fields of computer science and computational physics.

This second edition of a very popular two-volume work presents a thorough first course in analysis, leading from real numbers to such advanced topics as differential forms on manifolds; asymptotic methods; Fourier, Laplace, and Legendre transforms; elliptic functions; and distributions. Especially notable in this course are the clearly expressed orientation toward the natural sciences and the informal exploration of the essence and the roots of the basic concepts and theorems of calculus. Clarity of exposition is matched by a wealth of instructive exercises, problems, and fresh applications to areas seldom touched on in textbooks on real analysis. The main difference between the second and first editions is the addition of a series of appendices to each volume. There are six of them in the first volume and five in the second. The subjects of these appendices are diverse. They are meant to be useful to both students (in mathematics and physics) and teachers, who may be motivated by different goals. Some of the appendices are surveys, both prospective and retrospective. The final survey establishes important conceptual connections between analysis and other parts of mathematics. The first volume constitutes a complete course in one-variable calculus along with the multivariable differential calculus elucidated in an up-to-date, clear manner, with a pleasant geometric and natural sciences flavor.

Help students to develop their knowledge and build essential skills with practical assessment guidance and plenty of support for the new mathematical requirements in this updated, all-in-one textbook for Years 1 and 2. Combining everything your students need to know for the Pearson Edexcel A level Physics specification, this revised textbook will: - Support practical assessment with practical skill summaries throughout. - Provide support for all 16 required practicals with detailed explanations, data and exam style questions for students to answer. - Build understanding and knowledge with a variety of questions to engage and challenge students throughout the course: prior knowledge, worked examples, 'Test yourself' and exam practice questions. - Aid mathematical understanding and application with worked examples of calculations and a dedicated 'Maths for Physics' chapter. - Develop understanding and enable self- and peer-assessment with free online access to 'Test yourself' answers.

Key features: Provides a literature-based approach with examples of cutting-edge applications and the state of the art Presents the necessary theory as needed, chapter by chapter Synthesises concepts from physics and chemistry.

The 2nd edition of this book is essentially an extended version of the 1st and provides a very sound overview of the most important special functions of Fractional Calculus. It has been updated with material from many recent papers and includes several surveys of important results known before the publication of the 1st edition, but not covered there. As a result of researchers' and scientists' increasing interest in pure as well as applied mathematics in non-conventional models, particularly those using fractional calculus, Mittag-Leffler functions have caught the interest of the scientific community. Focusing on the theory of Mittag-Leffler functions, this volume offers a self-contained, comprehensive treatment, ranging from rather elementary matters to the latest research results. In addition to the theory the authors devote some sections of the work to applications, treating various situations and processes in viscoelasticity, physics, hydrodynamics, diffusion and wave phenomena, as well as stochastics. In particular, the Mittag-Leffler functions make it possible to describe phenomena in processes that progress or decay too slowly to be represented by classical functions like the exponential function and related special functions. The book is intended for a broad audience, comprising graduate students, university instructors and scientists in the field of pure and applied mathematics, as well as researchers in applied sciences like mathematical physics, theoretical chemistry, bio-mathematics, control theory and several other related areas.

This second English edition of a very popular two-volume work presents a thorough first course in analysis, leading from real numbers to such advanced topics as differential forms on manifolds; asymptotic methods; Fourier, Laplace, and Legendre transforms; elliptic functions; and distributions. Especially notable in this course are the clearly expressed orientation toward the natural sciences and the informal exploration of the essence and the roots of the basic concepts and theorems of calculus. Clarity of exposition is matched by a wealth of instructive exercises, problems, and fresh applications to areas seldom touched on in textbooks on real analysis. The main difference between the second and first English editions is the addition of a series of appendices to each volume. There are six of them in the first volume and five in the second. The subjects of these appendices are diverse. They are meant to be useful to both students (in mathematics and physics) and teachers, who may be motivated by different goals. Some of the appendices are surveys, both prospective and retrospective. The final survey establishes important conceptual connections between analysis and other parts of mathematics. This second volume presents classical analysis in its current form as part of a unified mathematics. It shows how analysis interacts with other modern fields of mathematics such as algebra, differential geometry, differential equations, complex analysis, and functional analysis. This book provides a firm foundation for advanced work in any of these directions.

This book highlights a concise and readable introduction to typical treatments of partial differential equations in mathematical physics. Mathematical physics is regarded by many as a profound discipline. In conventional textbooks of mathematical physics, the known and the new pieces of knowledge often intertwine with each other. The book aims to ease readers' struggle by facilitating a smooth transition to new knowledge. To achieve so, the author designs knowledge maps before each chapter and provides comparative summaries in each chapter whenever appropriate. Through these unique ways, readers can clarify the underlying structures among different equations and extend one's vision to the big picture. The book also emphasizes applications of the knowledge by providing practical examples. The book is intended for all those interested in mathematical physics, enabling them to develop a solid command in using partial differential equations to solve physics and engineering problems in a not-so-painful learning experience.

This book advocates the importance and value of errors for the progress of scientific research! Hans Kricheldorf explains that most of the great scientific achievements are based on an iterative process (an 'innate self-healing mechanism'): errors are committed, being checked over and over again, through which finally new findings and knowledge can arise. New ideas are often first confronted with refusal. This is so not only in real life, but also in scientific and medical research. The author outlines in this book how great ideas had to ripen over time before winning recognition and being accepted. The book showcases in an entertaining way, but without schadenfreude, that even some of the most famous discoverers may appear in completely different light, when regarding errors they have committed in their work. This book is divided into two parts. The first part creates a fundament for the discussion and understanding by introducing important concepts, terms and definitions, such as (natural) sciences and scientific research, laws of nature, paradigm shift, and progress (in science). It compares natural sciences with other scientific disciplines, such as historical research or sociology, and examines the question if scientific research can generate knowledge of permanent validity. The second part contains a collection of famous fallacies and errors from medicine, biology, chemistry, physics and geology, and how they were corrected. Readers will be astonished and intrigued what meanders had to be explored in some cases before scientists realized facts, which are today's standard and state-of-the-art of science and technology. This is an entertaining and amusing, but also highly informative book not only for scientists and specialists, but for everybody interested in science, research, their progress, and their history!

"A rich tightly woven tapestry of synchronicities; a true larger than life panoramic epic; an anthology of North Beach San Francisco writers created in "Super Vision" by Jack Sarfatti, the visionary physicist, who made "The Dancing Wu Li Masters" possible."

The book of nature is written in the language of mathematics Galileo Galilei, 1623 Metrology strives to supervise the ?ow of the measurand's true values throughconsecutive,arbitrarilyinterlockingseriesofmeasurements.Tohi- light this feature the term traceability has been coined. Traceability is said to be achieved, given the true values of each of the physical quantities entering and leaving the measurement are localized by speci?ed measu- ment uncertainties. The classical Gaussian error calculus is known to be con?ned to the tre- ment of random errors. Hence, there is no distinction between the true value of a measurand on the one side and the expectation of the respective es- mator on the other. This became apparent not until metrologists considered the e?ect of so-called unknown systematic errors. Unknown systematic errors are time-constant quantities unknown with respect to magnitude and sign. While random errors are treated via distribution densities, unknown syst- atic errors can only be assessed via intervals of estimated lengths. Unknown systematic errors were, in fact, addressed and discussed by Gauss himself. Gauss, however, argued that it were up to the experimenter to eliminate their causes and free the measured values from their in?uence.

This monograph is devoted to the theory and approximation by finite volume methods of nonlinear hyperbolic systems of conservation laws in one or two space variables. It follows directly a previous publication on hyperbolic systems of conservation laws by the same authors. Since the earlier work concentrated on the mathematical theory of multidimensional scalar conservation laws, this book will focus on systems and the theoretical aspects which are needed in the applications, such as the solution of the Riemann problem and further insights into more sophisticated problems, with special attention to the system of gas dynamics. This new edition includes more examples such as MHD and shallow water, with an insight on multiphase flows. Additionally, the text includes source terms and well-balanced/asymptotic preserving schemes, introducing relaxation schemes and addressing problems related to resonance and discontinuous fluxes while adding details on the low Mach number situation.

- Offers an abundance of explanations in a simple and clear manner without requiring mathematical knowledge above high school level - Presents thorough and detailed explanations of both General Relativity and Special Relativity - Presents simple demonstrations that are physically oriented and include complete explanations - Gives demonstrations of Special Relativity, including E=mc(2), and General Relativity, including the covariant derivative, the geodesic equation and the relativistic Maxwell laws

* Written by an interdisciplinary group of specialists from the arts, humanities and sciences at Oxford University * Suitable for a wide non-academic readership, and will appeal to anyone with an interest in mathematics, science and philosophy.

This monograph discusses recent advances in ergodic theory and dynamical systems. As a mixture of survey papers of active research areas and original research papers, this volume attracts young and senior researchers alike. Contents: Duality of the almost periodic and proximal relations Limit directions of a vector cocycle, remarks and examples Optimal norm approximation in ergodic theory The iterated Prisoner's Dilemma: good strategies and their dynamics Lyapunov exponents for conservative twisting dynamics: a survey Takens' embedding theorem with a continuous observable

Lie theory is a mathematical framework for encoding the concept of symmetries of a problem, and was the central theme of an INdAM intensive research period at the Centro de Giorgi in Pisa, Italy, in the academic year 2014-2015. This book gathers the key outcomes of this period, addressing topics such as: structure and representation theory of vertex algebras, Lie algebras and superalgebras, as well as hyperplane arrangements with different approaches, ranging from geometry and topology to combinatorics.

The eighth book of Aristotle's Physics is the culmination of his theory of nature. He discusses not just physics, but the origins of the universe and the metaphysical foundations of cosmology and physical science. He moves from the discussion of motion in the cosmos to the identification of a single source and regulating principle of all motion, and so argues for the existence of a first `unmoved mover'. Daniel Graham offers a clear, accurate new translation of this key text in the history of Western thought, and accompanies the translation with a careful philosophical commentary to guide the reader towards an understanding of the wealth of important and influential arguments and ideas that Aristotle puts forward.

This work can be recommended as an extensive course in superanalysis, the theory of functions of commuting and anticommuting variables. It follows the so-called functional superanalysis which was developed by J. Schwinger, B. De Witt, A. Rogers, V.S. Vladimirov and I.V. Volovich, Yu. Kobayashi and S. Nagamashi, M. Batchelor, U. Buzzo and R. Cianci and the present author. In this approach, superspace is defined as a set of points on which commuting and anticommuting coordinates are given. Thus functional superanalysis is a natural generalization of Newton's analysis (on real space) and strongly differs from the so-called algebraic analysis which has no functions of superpoints, and where functions' are just elements of Grassmann algebras. This volume is important for quantum physics in that it offers the possibility of extending the notion of space, and of operating on spaces which are described by noncommuting coordinates. These supercoordinates, which are described by an infinite number of ordinary real, complex or p-adic coordinates, are interpreted as creation or annihilation operators of quantum field theory. Subjects treated include differential calculus, including Cauchy-Riemann conditions, on superspaces over supercommutative Banach and topological superalgebras; integral calculus, including integration of differential forms; theory of distributions and linear partial differential equations with constant coefficients; calculus of pseudo-differential operators; analysis on infinite-dimensional superspaces over supercommutative Banach and topological supermodules; infinite-dimensional superdistributions and Feynman integrals with applications to superfield theory; noncommutativeprobabilities (central limit theorem); and non-Archimedean superanalysis. Audience: This volume will be of interest to researchers and postgraduate students whose work involves functional analysis, Feynman integration and distribution theory on infinite-dimensional (super)spaces and its applications to quantum physics, supersymmetry, superfield theory and supergravity.

A Concise Handbook of Mathematics, Physics, and Engineering Sciences takes a practical approach to the basic notions, formulas, equations, problems, theorems, methods, and laws that most frequently occur in scientific and engineering applications and university education. The authors pay special attention to issues that many engineers and students find difficult to understand. The first part of the book contains chapters on arithmetic, elementary and analytic geometry, algebra, differential and integral calculus, functions of complex variables, integral transforms, ordinary and partial differential equations, special functions, and probability theory. The second part discusses molecular physics and thermodynamics, electricity and magnetism, oscillations and waves, optics, special relativity, quantum mechanics, atomic and nuclear physics, and elementary particles. The third part covers dimensional analysis and similarity, mechanics of point masses and rigid bodies, strength of materials, hydrodynamics, mass and heat transfer, electrical engineering, and methods for constructing empirical and engineering formulas. The main text offers a concise, coherent survey of the most important definitions, formulas, equations, methods, theorems, and laws. Numerous examples throughout and references at the end of each chapter provide readers with a better understanding of the topics and methods. Additional issues of interest can be found in the remarks. For ease of reading, the supplement at the back of the book provides several long mathematical tables, including indefinite and definite integrals, direct and inverse integral transforms, and exact solutions of differential equations.

Aims at the research of a physics model based on an advanced thinking paradigm Presents deep-going solutions along with a richer connotation Contains fully analyzed models Deeply resolves and expands some classical physics models into novel questions Optimizes many existing solutions to the classical questions and even provides novel solutions to classic models and common questions Draws clearer, detailed, and exquisite schematic illustrations for all physical models

"Blurb & Contents" Frank von Hippel has been at the forefront of those scientists grappling with the troubled legacy of our Nuclear Age. Von Hippel offers insights about the choices we must make and how science can help us to make them. Topics include nuclear power, atomic weapons, disarmament, energy and the future of automobiles. The scientist's role in public life and the importance of "making trouble" is emphasized. Of interest to physicists, particularly those working in nuclear physics, policy makers, environmentalists and those concerned with nuclear disarmament and the role of science in society.

Over the course of his distinguished career, Vladimir Maz'ya has made a number of groundbreaking contributions to numerous areas of mathematics, including partial differential equations, function theory, and harmonic analysis. The chapters in this volume - compiled on the occasion of his 80th birthday - are written by distinguished mathematicians and pay tribute to his many significant and lasting achievements.